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href="#By_type_of_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>By type of notation</span> </div> </a> <button aria-controls="toc-By_type_of_notation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle By type of notation subsection</span> </button> <ul id="toc-By_type_of_notation-sublist" class="vector-toc-list"> <li id="toc-Standard_positional_numeral_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standard_positional_numeral_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Standard positional numeral systems</span> </div> </a> <ul id="toc-Standard_positional_numeral_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-standard_positional_numeral_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-standard_positional_numeral_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Non-standard positional numeral systems</span> </div> </a> <ul id="toc-Non-standard_positional_numeral_systems-sublist" class="vector-toc-list"> <li id="toc-Bijective_numeration" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bijective_numeration"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Bijective numeration</span> </div> </a> <ul id="toc-Bijective_numeration-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Signed-digit_representation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Signed-digit_representation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Signed-digit representation</span> </div> </a> <ul id="toc-Signed-digit_representation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complex_bases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complex_bases"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Complex bases</span> </div> </a> <ul id="toc-Complex_bases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-integer_bases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Non-integer_bases"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.4</span> <span>Non-integer bases</span> </div> </a> <ul id="toc-Non-integer_bases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-n-adic_number" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#n-adic_number"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.5</span> <span><i>n</i>-adic number</span> </div> </a> <ul id="toc-n-adic_number-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mixed_radix" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Mixed_radix"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.6</span> <span>Mixed radix</span> </div> </a> <ul id="toc-Mixed_radix-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.7</span> <span>Other</span> </div> </a> <ul id="toc-Other-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Non-positional_notation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-positional_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Non-positional notation</span> </div> </a> <ul id="toc-Non-positional_notation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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.sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Numeral_systems" title="Category:Numeral systems">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Numeral_system" title="Numeral system">Numeral systems</a></th></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Positional_notation" title="Positional notation">Place-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numerals</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Arabic_numerals" title="Arabic numerals">Western Arabic</a></li> <li><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic</a></li></ul> <hr /> <ul><li><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali</a></li> <li><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari</a></li> <li><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati</a></li> <li><a href="/wiki/Gurmukhi_numerals" class="mw-redirect" title="Gurmukhi numerals">Gurmukhi</a></li> <li><a href="/wiki/Odia_numerals" title="Odia numerals">Odia</a></li> <li><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala</a></li> <li><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil</a></li> <li><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam</a></li> <li><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu</a></li> <li><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada</a></li> <li><a href="/wiki/Dzongkha_numerals" title="Dzongkha numerals">Dzongkha</a></li></ul> <hr /> <ul><li><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan</a></li> <li><a href="/wiki/Balinese_numerals" title="Balinese numerals">Balinese</a></li> <li><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese</a></li> <li><a href="/wiki/Javanese_numerals" title="Javanese numerals">Javanese</a></li> <li><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer</a></li> <li><a href="/wiki/Lao_script#Numerals" title="Lao script">Lao</a></li> <li><a href="/wiki/Mongolian_numerals" title="Mongolian numerals">Mongolian</a></li> <li><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese</a></li> <li><a href="/wiki/Thai_numerals" title="Thai numerals">Thai</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">East Asian systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> <ul><li><a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou</a></li></ul></li> <li><a href="/wiki/Hokkien_numerals" title="Hokkien numerals">Hokkien</a></li> <li><a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese</a></li> <li><a href="/wiki/Korean_numerals" title="Korean numerals">Korean</a></li> <li><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese</a></li></ul> <hr /> <dl><dt>Historic</dt></dl> <ul><li><a href="/wiki/Counting_rods" title="Counting rods">Counting rods</a></li> <li><a href="/wiki/Tangut_numerals" title="Tangut numerals">Tangut</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Other systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">History</a></li></ul> <hr /> <dl><dt><a href="/wiki/Ancient_history" title="Ancient history">Ancient</a></dt></dl> <ul><li><a href="/wiki/Babylonian_cuneiform_numerals" title="Babylonian cuneiform numerals">Babylonian</a></li></ul> <hr /> <dl><dt><a href="/wiki/Post-classical_history" title="Post-classical history">Post-classical</a></dt></dl> <ul><li><a href="/wiki/Cistercian_numerals" title="Cistercian numerals">Cistercian</a></li> <li><a href="/wiki/Maya_numerals" title="Maya numerals">Mayan</a></li> <li><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a></li> <li><a href="/wiki/Pentadic_numerals" title="Pentadic numerals">Pentadic</a></li> <li><a href="/wiki/Quipu" title="Quipu">Quipu</a></li> <li><a href="/wiki/Rumi_Numeral_Symbols" title="Rumi Numeral Symbols">Rumi</a></li></ul> <hr /> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Cherokee_syllabary#Numerals" title="Cherokee syllabary">Cherokee</a></li> <li><a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik</a> (Iñupiaq)</li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">By <a href="/wiki/Radix" title="Radix">radix/base</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Common radices/bases</dt></dl> <ul><li><a href="/wiki/Binary_number" title="Binary number">2</a></li> <li><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">3</a></li> <li><a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">4</a></li> <li><a href="/wiki/Quinary" title="Quinary">5</a></li> <li><a href="/wiki/Senary" title="Senary">6</a></li> <li><a href="/wiki/Octal" title="Octal">8</a></li> <li><a href="/wiki/Decimal" title="Decimal">10</a></li> <li><a href="/wiki/Duodecimal" title="Duodecimal">12</a></li> <li><a href="/wiki/Hexadecimal" title="Hexadecimal">16</a></li> <li><a href="/wiki/Vigesimal" title="Vigesimal">20</a></li> <li><a href="/wiki/Sexagesimal" title="Sexagesimal">60</a></li></ul> <hr /> <dl><dt><a href="/wiki/Non-standard_positional_numeral_systems" title="Non-standard positional numeral systems">Non-standard radices/bases</a></dt></dl> <ul><li><a href="/wiki/Bijective_numeration" title="Bijective numeration">Bijective</a><span class="nowrap"> </span>(<a href="/wiki/Unary_numeral_system" title="Unary numeral system">1</a>)</li> <li><a href="/wiki/Signed-digit_representation" title="Signed-digit representation">Signed-digit</a><span class="nowrap"> </span>(<a href="/wiki/Balanced_ternary" title="Balanced ternary">balanced ternary</a>)</li> <li><a href="/wiki/Mixed_radix" title="Mixed radix">Mixed</a><span class="nowrap"> </span>(<a href="/wiki/Factorial_number_system" title="Factorial number system">factorial</a>)</li> <li><a href="/wiki/Negative_base" title="Negative base">Negative</a></li> <li><a href="/wiki/Complex-base_system" title="Complex-base system">Complex</a><span class="nowrap"> </span>(<a href="/wiki/Quater-imaginary_base" title="Quater-imaginary base">2<i>i</i></a>)</li> <li><a href="/wiki/Non-integer_base_of_numeration" title="Non-integer base of numeration">Non-integer</a><span class="nowrap"> </span>(<a href="/wiki/Golden_ratio_base" title="Golden ratio base">φ</a>)</li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric</a></li></ul></div></div></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Sign-value_notation" title="Sign-value notation">Sign-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Non-alphabetic</dt></dl> <ul><li><a href="/wiki/Aegean_numerals" title="Aegean numerals">Aegean</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic</a></li> <li><a href="/wiki/Aztec_script#Numerals" title="Aztec script">Aztec</a></li> <li><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi</a></li> <li><a href="/wiki/Chuvash_numerals" title="Chuvash numerals">Chuvash</a></li> <li><a href="/wiki/Egyptian_numerals" title="Egyptian numerals">Egyptian</a></li> <li><a href="/wiki/Etruscan_numerals" title="Etruscan numerals">Etruscan</a></li> <li><a href="/wiki/Kharosthi_numerals" class="mw-redirect" title="Kharosthi numerals">Kharosthi</a></li> <li><a href="/wiki/Prehistoric_counting" title="Prehistoric counting">Prehistoric counting</a></li> <li><a href="/wiki/Proto-cuneiform" title="Proto-cuneiform">Proto-cuneiform</a></li> <li><a href="/wiki/Roman_numerals" title="Roman numerals">Roman</a></li> <li><a href="/wiki/Tally_marks" title="Tally marks">Tally marks</a></li></ul> <hr /> <dl><dt><a href="/wiki/Alphabetic_numeral_system" title="Alphabetic numeral system">Alphabetic</a></dt></dl> <ul><li><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad</a></li> <li><a href="/wiki/Armenian_numerals" title="Armenian numerals">Armenian</a></li> <li><a href="/wiki/Alphasyllabic_numeral_system" title="Alphasyllabic numeral system">Alphasyllabic</a> <ul><li><a href="/wiki/Aksharapalli" title="Aksharapalli">Akṣarapallī</a></li> <li><a href="/wiki/%C4%80ryabha%E1%B9%ADa_numeration" title="Āryabhaṭa numeration">Āryabhaṭa</a></li> <li><a href="/wiki/Katapayadi_system" title="Katapayadi system">Kaṭapayādi</a></li></ul></li> <li><a href="/wiki/Coptic_numerals" class="mw-redirect" title="Coptic numerals">Coptic</a></li> <li><a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic</a></li> <li><a href="/wiki/Ge%CA%BDez_script#Numerals" title="Geʽez script">Geʽez</a></li> <li><a href="/wiki/Georgian_numerals" title="Georgian numerals">Georgian</a></li> <li><a href="/wiki/Glagolitic_numerals" title="Glagolitic numerals">Glagolitic</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek</a></li> <li><a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <a class="mw-selflink selflink">List of numeral systems</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Numeral_systems" title="Template:Numeral systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Numeral_systems" title="Template talk:Numeral systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Numeral_systems" title="Special:EditPage/Template:Numeral systems"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1092331828">@media(min-width:720px){.mw-parser-output .contains-special-characters{width:22em}}</style><div class="side-box metadata side-box-right contains-special-characters noprint selfref"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="skin-invert" typeof="mw:File"><a href="/wiki/Specials_(Unicode_block)#Replacement_character" title="Specials (Unicode block)"><img alt="<?>" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Replacement_character.svg/40px-Replacement_character.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Replacement_character.svg/60px-Replacement_character.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Replacement_character.svg/80px-Replacement_character.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span></div> <div class="side-box-text plainlist"><b>This article contains uncommon <a href="/wiki/Unicode" title="Unicode">Unicode</a> characters.</b> Without proper <a href="/wiki/Help:Multilingual_support" title="Help:Multilingual support">rendering support</a>, you may see <a href="/wiki/Specials_(Unicode_block)#Replacement_character" title="Specials (Unicode block)">question marks, boxes, or other symbols</a> instead of the intended characters.</div></div> </div> <p>There are many different <a href="/wiki/Numeral_system" title="Numeral system">numeral systems</a>, that is, <a href="/wiki/Writing_system" title="Writing system">writing systems</a> for expressing <a href="/wiki/Numbers" class="mw-redirect" title="Numbers">numbers</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="By_culture_/_time_period"><span id="By_culture_.2F_time_period"></span>By culture / time period</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=1" title="Edit section: By culture / time period"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>"A <i>base</i> is a natural number B whose <i>powers</i> (B multiplied by itself some number of times) are specially designated within a numerical system."<sup id="cite_ref-Chrisomalis2004_1-0" class="reference"><a href="#cite_note-Chrisomalis2004-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 38">: 38 </span></sup> The term is not equivalent to <a href="/wiki/Radix" title="Radix">radix</a>, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers.<sup id="cite_ref-Chrisomalis2004_1-1" class="reference"><a href="#cite_note-Chrisomalis2004-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base). </p> <table class="wikitable sortable"> <tbody><tr> <th>Name </th> <th data-sort-type="number">Base </th> <th>Sample </th> <th data-sort-type="number">Approx. First Appearance </th></tr> <tr> <td><a href="/wiki/Proto-cuneiform_numerals" class="mw-redirect" title="Proto-cuneiform numerals">Proto-cuneiform numerals</a></td> <td>10<span style="font-size:88%;">&</span>60</td> <td></td> <td><span data-sort-value="-3500 !">c. 3500–2000 BCE</span> </td></tr> <tr> <td><a href="/wiki/Indus_script" title="Indus script">Indus numerals</a></td> <td>unknown<sup id="cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]_2-0" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></td> <td></td> <td><span data-sort-value="-3501 !">c. 3500–1900 BCE</span><sup id="cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]_2-1" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Proto-Elamite#Proto-Elamite_script" class="mw-redirect" title="Proto-Elamite">Proto-Elamite numerals</a></td> <td>10<span style="font-size:88%;">&</span>60</td> <td></td> <td><span data-sort-value="-3101 !">3100 BCE</span> </td></tr> <tr> <td><a href="/wiki/Sumerian_numerals" class="mw-redirect" title="Sumerian numerals">Sumerian numerals</a></td> <td>10<span style="font-size:88%;">&</span>60</td> <td></td> <td><span data-sort-value="-3100 !">3100 BCE</span> </td></tr> <tr> <td><a href="/wiki/Egyptian_numerals" title="Egyptian numerals">Egyptian numerals</a></td> <td>10</td> <td><table class="mw-hiero-table mw-hiero-outer" dir="ltr"><tbody><tr><td> <table class="mw-hiero-table"><tbody><tr> <td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_Z1.png?4dc06" height="16" title="Z1" alt="Z1" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_V20.png?e78cb" height="13" title="V20" alt="V20" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_V1.png?25c3d" height="20" title="V1" alt="V1" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_M12.png?2f65f" height="38" title="M12" alt="M12" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_D50.png?c9db5" height="38" title="D50" alt="D50" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_I8.png?41a9e" height="38" title="I8" alt="I8" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_I7.png?d5b8f" height="28" title="I7" alt="I7" /></td><td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_C11.png?7c116" height="38" title="C11" alt="C11" /></td></tr></tbody></table> </td></tr></tbody></table></td> <td><span data-sort-value="-3000 !">3000 BCE</span> </td></tr> <tr> <td><a href="/wiki/Babylonian_numerals" class="mw-redirect" title="Babylonian numerals">Babylonian numerals</a></td> <td>10<span style="font-size:88%;">&</span>60</td> <td><span typeof="mw:File"><a href="/wiki/File:Babylonian_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Babylonian_1.svg/15px-Babylonian_1.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Babylonian_1.svg/23px-Babylonian_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Babylonian_1.svg/30px-Babylonian_1.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Babylonian_2.svg/15px-Babylonian_2.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Babylonian_2.svg/23px-Babylonian_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Babylonian_2.svg/30px-Babylonian_2.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Babylonian_3.svg/15px-Babylonian_3.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Babylonian_3.svg/23px-Babylonian_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Babylonian_3.svg/30px-Babylonian_3.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Babylonian_4.svg/15px-Babylonian_4.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Babylonian_4.svg/23px-Babylonian_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Babylonian_4.svg/30px-Babylonian_4.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Babylonian_5.svg/15px-Babylonian_5.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Babylonian_5.svg/23px-Babylonian_5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Babylonian_5.svg/30px-Babylonian_5.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Babylonian_6.svg/15px-Babylonian_6.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Babylonian_6.svg/23px-Babylonian_6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Babylonian_6.svg/30px-Babylonian_6.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Babylonian_7.svg/15px-Babylonian_7.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Babylonian_7.svg/23px-Babylonian_7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Babylonian_7.svg/30px-Babylonian_7.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_8.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Babylonian_8.svg/15px-Babylonian_8.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Babylonian_8.svg/23px-Babylonian_8.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Babylonian_8.svg/30px-Babylonian_8.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_9.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Babylonian_9.svg/15px-Babylonian_9.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Babylonian_9.svg/23px-Babylonian_9.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Babylonian_9.svg/30px-Babylonian_9.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span> <span typeof="mw:File"><a href="/wiki/File:Babylonian_10.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Babylonian_10.svg/15px-Babylonian_10.svg.png" decoding="async" width="15" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Babylonian_10.svg/23px-Babylonian_10.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Babylonian_10.svg/30px-Babylonian_10.svg.png 2x" data-file-width="144" data-file-height="135" /></a></span></td> <td><span data-sort-value="-2000 !">2000 BCE</span> </td></tr> <tr> <td><a href="/wiki/Aegean_numerals" title="Aegean numerals">Aegean numerals</a></td> <td>10</td> <td>𐄇 𐄈 𐄉 𐄊 𐄋 𐄌 𐄍 𐄎 𐄏  ( <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_1.svg" class="mw-file-description" title="1"><img alt="1" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Aegean_numeral_1.svg/10px-Aegean_numeral_1.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Aegean_numeral_1.svg/15px-Aegean_numeral_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Aegean_numeral_1.svg/20px-Aegean_numeral_1.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_2.svg" class="mw-file-description" title="2"><img alt="2" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Aegean_numeral_2.svg/10px-Aegean_numeral_2.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Aegean_numeral_2.svg/15px-Aegean_numeral_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Aegean_numeral_2.svg/20px-Aegean_numeral_2.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_3.svg" class="mw-file-description" title="3"><img alt="3" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Aegean_numeral_3.svg/10px-Aegean_numeral_3.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Aegean_numeral_3.svg/15px-Aegean_numeral_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Aegean_numeral_3.svg/20px-Aegean_numeral_3.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_4.svg" class="mw-file-description" title="4"><img alt="4" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Aegean_numeral_4.svg/10px-Aegean_numeral_4.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Aegean_numeral_4.svg/15px-Aegean_numeral_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Aegean_numeral_4.svg/20px-Aegean_numeral_4.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_5.svg" class="mw-file-description" title="5"><img alt="5" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Aegean_numeral_5.svg/10px-Aegean_numeral_5.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Aegean_numeral_5.svg/15px-Aegean_numeral_5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Aegean_numeral_5.svg/20px-Aegean_numeral_5.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_6.svg" class="mw-file-description" title="6"><img alt="6" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Aegean_numeral_6.svg/10px-Aegean_numeral_6.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Aegean_numeral_6.svg/15px-Aegean_numeral_6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Aegean_numeral_6.svg/20px-Aegean_numeral_6.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_7.svg" class="mw-file-description" title="7"><img alt="7" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_7.svg/10px-Aegean_numeral_7.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_7.svg/15px-Aegean_numeral_7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_7.svg/20px-Aegean_numeral_7.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_8.svg" class="mw-file-description" title="8"><img alt="8" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Aegean_numeral_8.svg/10px-Aegean_numeral_8.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Aegean_numeral_8.svg/15px-Aegean_numeral_8.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Aegean_numeral_8.svg/20px-Aegean_numeral_8.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_9.svg" class="mw-file-description" title="9"><img alt="9" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Aegean_numeral_9.svg/10px-Aegean_numeral_9.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Aegean_numeral_9.svg/15px-Aegean_numeral_9.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Aegean_numeral_9.svg/20px-Aegean_numeral_9.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> )<br /> 𐄐 𐄑 𐄒 𐄓 𐄔 𐄕 𐄖 𐄗 𐄘  ( <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_10.svg" class="mw-file-description" title="10"><img alt="10" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_10.svg/10px-Aegean_numeral_10.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_10.svg/15px-Aegean_numeral_10.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Aegean_numeral_10.svg/20px-Aegean_numeral_10.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_20.svg" class="mw-file-description" title="20"><img alt="20" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Aegean_numeral_20.svg/10px-Aegean_numeral_20.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Aegean_numeral_20.svg/15px-Aegean_numeral_20.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Aegean_numeral_20.svg/20px-Aegean_numeral_20.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_30.svg" class="mw-file-description" title="30"><img alt="30" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Aegean_numeral_30.svg/10px-Aegean_numeral_30.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Aegean_numeral_30.svg/15px-Aegean_numeral_30.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Aegean_numeral_30.svg/20px-Aegean_numeral_30.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_40.svg" class="mw-file-description" title="40"><img alt="40" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Aegean_numeral_40.svg/10px-Aegean_numeral_40.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Aegean_numeral_40.svg/15px-Aegean_numeral_40.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Aegean_numeral_40.svg/20px-Aegean_numeral_40.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_50.svg" class="mw-file-description" title="50"><img alt="50" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Aegean_numeral_50.svg/10px-Aegean_numeral_50.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Aegean_numeral_50.svg/15px-Aegean_numeral_50.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Aegean_numeral_50.svg/20px-Aegean_numeral_50.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_60.svg" class="mw-file-description" title="60"><img alt="60" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Aegean_numeral_60.svg/10px-Aegean_numeral_60.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Aegean_numeral_60.svg/15px-Aegean_numeral_60.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Aegean_numeral_60.svg/20px-Aegean_numeral_60.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_70.svg" class="mw-file-description" title="70"><img alt="70" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Aegean_numeral_70.svg/10px-Aegean_numeral_70.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Aegean_numeral_70.svg/15px-Aegean_numeral_70.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Aegean_numeral_70.svg/20px-Aegean_numeral_70.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_80.svg" class="mw-file-description" title="80"><img alt="80" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Aegean_numeral_80.svg/10px-Aegean_numeral_80.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Aegean_numeral_80.svg/15px-Aegean_numeral_80.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Aegean_numeral_80.svg/20px-Aegean_numeral_80.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_90.svg" class="mw-file-description" title="90"><img alt="90" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Aegean_numeral_90.svg/10px-Aegean_numeral_90.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Aegean_numeral_90.svg/15px-Aegean_numeral_90.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Aegean_numeral_90.svg/20px-Aegean_numeral_90.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> )<br /> 𐄙 𐄚 𐄛 𐄜 𐄝 𐄞 𐄟 𐄠 𐄡  ( <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_100.svg" class="mw-file-description" title="100"><img alt="100" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aegean_numeral_100.svg/10px-Aegean_numeral_100.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aegean_numeral_100.svg/15px-Aegean_numeral_100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aegean_numeral_100.svg/20px-Aegean_numeral_100.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_200.svg" class="mw-file-description" title="200"><img alt="200" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Aegean_numeral_200.svg/10px-Aegean_numeral_200.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Aegean_numeral_200.svg/15px-Aegean_numeral_200.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Aegean_numeral_200.svg/20px-Aegean_numeral_200.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_300.svg" class="mw-file-description" title="300"><img alt="300" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Aegean_numeral_300.svg/10px-Aegean_numeral_300.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Aegean_numeral_300.svg/15px-Aegean_numeral_300.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Aegean_numeral_300.svg/20px-Aegean_numeral_300.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_400.svg" class="mw-file-description" title="400"><img alt="400" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Aegean_numeral_400.svg/10px-Aegean_numeral_400.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Aegean_numeral_400.svg/15px-Aegean_numeral_400.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Aegean_numeral_400.svg/20px-Aegean_numeral_400.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_500.svg" class="mw-file-description" title="500"><img alt="500" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Aegean_numeral_500.svg/10px-Aegean_numeral_500.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Aegean_numeral_500.svg/15px-Aegean_numeral_500.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Aegean_numeral_500.svg/20px-Aegean_numeral_500.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_600.svg" class="mw-file-description" title="600"><img alt="600" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_600.svg/10px-Aegean_numeral_600.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_600.svg/15px-Aegean_numeral_600.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_600.svg/20px-Aegean_numeral_600.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_700.svg" class="mw-file-description" title="700"><img alt="700" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Aegean_numeral_700.svg/10px-Aegean_numeral_700.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Aegean_numeral_700.svg/15px-Aegean_numeral_700.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Aegean_numeral_700.svg/20px-Aegean_numeral_700.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_800.svg" class="mw-file-description" title="800"><img alt="800" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Aegean_numeral_800.svg/10px-Aegean_numeral_800.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Aegean_numeral_800.svg/15px-Aegean_numeral_800.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Aegean_numeral_800.svg/20px-Aegean_numeral_800.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_900.svg" class="mw-file-description" title="900"><img alt="900" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Aegean_numeral_900.svg/10px-Aegean_numeral_900.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Aegean_numeral_900.svg/15px-Aegean_numeral_900.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Aegean_numeral_900.svg/20px-Aegean_numeral_900.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> )<br /> 𐄢 𐄣 𐄤 𐄥 𐄦 𐄧 𐄨 𐄩 𐄪  ( <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_1000.svg" class="mw-file-description" title="1000"><img alt="1000" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Aegean_numeral_1000.svg/10px-Aegean_numeral_1000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Aegean_numeral_1000.svg/15px-Aegean_numeral_1000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Aegean_numeral_1000.svg/20px-Aegean_numeral_1000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_2000.svg" class="mw-file-description" title="2000"><img alt="2000" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aegean_numeral_2000.svg/10px-Aegean_numeral_2000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aegean_numeral_2000.svg/15px-Aegean_numeral_2000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aegean_numeral_2000.svg/20px-Aegean_numeral_2000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_3000.svg" class="mw-file-description" title="3000"><img alt="3000" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Aegean_numeral_3000.svg/10px-Aegean_numeral_3000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Aegean_numeral_3000.svg/15px-Aegean_numeral_3000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Aegean_numeral_3000.svg/20px-Aegean_numeral_3000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_4000.svg" class="mw-file-description" title="4000"><img alt="4000" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Aegean_numeral_4000.svg/10px-Aegean_numeral_4000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Aegean_numeral_4000.svg/15px-Aegean_numeral_4000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Aegean_numeral_4000.svg/20px-Aegean_numeral_4000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_5000.svg" class="mw-file-description" title="5000"><img alt="5000" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_5000.svg/10px-Aegean_numeral_5000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_5000.svg/15px-Aegean_numeral_5000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Aegean_numeral_5000.svg/20px-Aegean_numeral_5000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_6000.svg" class="mw-file-description" title="6000"><img alt="6000" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Aegean_numeral_6000.svg/10px-Aegean_numeral_6000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Aegean_numeral_6000.svg/15px-Aegean_numeral_6000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Aegean_numeral_6000.svg/20px-Aegean_numeral_6000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_7000.svg" class="mw-file-description" title="7000"><img alt="7000" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Aegean_numeral_7000.svg/10px-Aegean_numeral_7000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Aegean_numeral_7000.svg/15px-Aegean_numeral_7000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Aegean_numeral_7000.svg/20px-Aegean_numeral_7000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_8000.svg" class="mw-file-description" title="8000"><img alt="8000" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Aegean_numeral_8000.svg/10px-Aegean_numeral_8000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Aegean_numeral_8000.svg/15px-Aegean_numeral_8000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Aegean_numeral_8000.svg/20px-Aegean_numeral_8000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_9000.svg" class="mw-file-description" title="9000"><img alt="9000" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Aegean_numeral_9000.svg/10px-Aegean_numeral_9000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Aegean_numeral_9000.svg/15px-Aegean_numeral_9000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Aegean_numeral_9000.svg/20px-Aegean_numeral_9000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> )<br /> 𐄫 𐄬 𐄭 𐄮 𐄯 𐄰 𐄱 𐄲 𐄳  ( <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_10000.svg" class="mw-file-description" title="10000"><img alt="10000" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Aegean_numeral_10000.svg/10px-Aegean_numeral_10000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Aegean_numeral_10000.svg/15px-Aegean_numeral_10000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Aegean_numeral_10000.svg/20px-Aegean_numeral_10000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_20000.svg" class="mw-file-description" title="20000"><img alt="20000" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Aegean_numeral_20000.svg/10px-Aegean_numeral_20000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Aegean_numeral_20000.svg/15px-Aegean_numeral_20000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Aegean_numeral_20000.svg/20px-Aegean_numeral_20000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_30000.svg" class="mw-file-description" title="30000"><img alt="30000" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Aegean_numeral_30000.svg/10px-Aegean_numeral_30000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Aegean_numeral_30000.svg/15px-Aegean_numeral_30000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Aegean_numeral_30000.svg/20px-Aegean_numeral_30000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_40000.svg" class="mw-file-description" title="40000"><img alt="40000" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Aegean_numeral_40000.svg/10px-Aegean_numeral_40000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Aegean_numeral_40000.svg/15px-Aegean_numeral_40000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Aegean_numeral_40000.svg/20px-Aegean_numeral_40000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_50000.svg" class="mw-file-description" title="50000"><img alt="50000" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Aegean_numeral_50000.svg/10px-Aegean_numeral_50000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Aegean_numeral_50000.svg/15px-Aegean_numeral_50000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Aegean_numeral_50000.svg/20px-Aegean_numeral_50000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_60000.svg" class="mw-file-description" title="60000"><img alt="60000" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Aegean_numeral_60000.svg/10px-Aegean_numeral_60000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Aegean_numeral_60000.svg/15px-Aegean_numeral_60000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Aegean_numeral_60000.svg/20px-Aegean_numeral_60000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_70000.svg" class="mw-file-description" title="70000"><img alt="70000" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Aegean_numeral_70000.svg/10px-Aegean_numeral_70000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Aegean_numeral_70000.svg/15px-Aegean_numeral_70000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Aegean_numeral_70000.svg/20px-Aegean_numeral_70000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_80000.svg" class="mw-file-description" title="80000"><img alt="80000" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Aegean_numeral_80000.svg/10px-Aegean_numeral_80000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Aegean_numeral_80000.svg/15px-Aegean_numeral_80000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Aegean_numeral_80000.svg/20px-Aegean_numeral_80000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> <span typeof="mw:File/Frameless"><a href="/wiki/File:Aegean_numeral_90000.svg" class="mw-file-description" title="90000"><img alt="90000" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Aegean_numeral_90000.svg/10px-Aegean_numeral_90000.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Aegean_numeral_90000.svg/15px-Aegean_numeral_90000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Aegean_numeral_90000.svg/20px-Aegean_numeral_90000.svg.png 2x" data-file-width="71" data-file-height="71" /></a></span> )</td> <td><span data-sort-value="-1500 !">1500 BCE</span> </td></tr> <tr> <td><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese numerals</a><br /><a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese numerals</a><br /><a href="/wiki/Korean_numerals" title="Korean numerals">Korean numerals</a> (<a href="/wiki/Sino-Korean_vocabulary" title="Sino-Korean vocabulary">Sino-Korean</a>)<br /><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese numerals</a> (<a href="/wiki/Sino-Vietnamese_vocabulary" title="Sino-Vietnamese vocabulary">Sino-Vietnamese</a>)</td> <td>10</td> <td> <p>零一二三四五六七八九十百千萬億 (Default, <a href="/wiki/Traditional_Chinese" class="mw-redirect" title="Traditional Chinese">Traditional Chinese</a>)<br /> 〇一二三四五六七八九十百千万亿 (Default, <a href="/wiki/Simplified_Chinese" class="mw-redirect" title="Simplified Chinese">Simplified Chinese</a>) </p> </td> <td><span data-sort-value="-1300 !">1300 BCE</span> </td></tr> <tr> <td><a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a></td> <td>5<span style="font-size:88%;">&</span>10</td> <td>I V X L C D M</td> <td><span data-sort-value="-1000 !">1000 BCE</span><sup id="cite_ref-Chrisomalis2004_1-2" class="reference"><a href="#cite_note-Chrisomalis2004-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew numerals</a></td> <td>10</td> <td><style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">א ב ג ד ה ו ז ח ט<br />י כ ל מ נ ס ע פ צ<br />ק ר ש ת ך ם ן ף ץ</span></td> <td><span data-sort-value="-800 !">800 BCE</span> </td></tr> <tr> <td><a href="/wiki/Indian_numerals" class="mw-redirect" title="Indian numerals">Indian numerals</a></td> <td>10</td> <td> <p><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali</a> ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ৯ </p><p><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari</a> ० १ २ ३ ४ ५ ६ ७ ८ ९ </p><p><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati</a> ૦ ૧ ૨ ૩ ૪ ૫ ૬ ૭ ૮ ૯ </p><p><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada</a> ೦ ೧ ೨ ೩ ೪ ೫ ೬ ೭ ೮ ೯ </p><p><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam</a> ൦ ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯ </p><p><a href="/wiki/Odia_numerals" title="Odia numerals">Odia</a> ୦ ୧ ୨ ୩ ୪ ୫ ୬ ୭ ୮ ୯ </p><p><a href="/wiki/Punjabi_language" title="Punjabi language">Punjabi</a> ੦ ੧ ੨ ੩ ੪ ੫ ੬ ੭ ੮ ੯ </p><p><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil</a> ௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯ </p><p><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu</a> ౦ ౧ ౨ ౩ ౪ ౫ ౬ ౭ ౮ ౯ </p><p><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan</a> <big>༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩</big> </p><p><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Urdu</a> <big>۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹</big> </p> </td> <td><span data-sort-value="-750 !">750–500 BCE</span> </td></tr> <tr> <td><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></td> <td>10</td> <td>ō α β γ δ ε ϝ ζ η θ ι <br /> ο Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ</td> <td><span data-sort-value="-400 !"><400 BCE</span> </td></tr> <tr> <td><a href="/wiki/Kharosthi" title="Kharosthi">Kharosthi numerals</a> </td> <td>4<span style="font-size:88%;">&</span>10 </td> <td>𐩇 𐩆 𐩅 𐩄 𐩃 𐩂 𐩁 𐩀 </td> <td><span data-sort-value="-401 !"><400–250 BCE</span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Phoenician_alphabet#Numerals" title="Phoenician alphabet">Phoenician numerals</a></td> <td>10</td> <td>𐤙 𐤘 𐤗 𐤛𐤛𐤛 𐤛𐤛𐤚 𐤛𐤛𐤖 𐤛𐤛 𐤛𐤚 𐤛𐤖 𐤛 𐤚 𐤖 <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="-250 !"><250 BCE</span><sup id="cite_ref-Cajori_5-0" class="reference"><a href="#cite_note-Cajori-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>Chinese <a href="/wiki/Rod_numerals" class="mw-redirect" title="Rod numerals">rod numerals</a></td> <td>10</td> <td>𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩</td> <td><span data-sort-value="1 !">1st Century</span> </td></tr> <tr> <td><a href="/wiki/Coptic_alphabet#Numerals" class="mw-redirect" title="Coptic alphabet">Coptic numerals</a></td> <td>10</td> <td>Ⲁ Ⲃ Ⲅ Ⲇ Ⲉ Ⲋ Ⲍ Ⲏ Ⲑ</td> <td><span data-sort-value="100 !">2nd Century</span> </td></tr> <tr> <td><a href="/wiki/Ge%27ez_numerals" class="mw-redirect" title="Ge'ez numerals">Ge'ez numerals</a></td> <td>10</td> <td>፩ ፪ ፫ ፬ ፭ ፮ ፯ ፰ ፱ <br /> ፲ ፳ ፴ ፵ ፶ ፷ ፸ ፹ ፺ <br /> ፻ <br /> ፼ <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="200 !">3rd–4th Century</span><br />15th Century (Modern Style)<sup id="cite_ref-Chrisomalis2010_7-0" class="reference"><a href="#cite_note-Chrisomalis2010-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 135–136">: 135–136 </span></sup> </td></tr> <tr> <td><a href="/wiki/Armenian_numerals" title="Armenian numerals">Armenian numerals</a></td> <td>10</td> <td>Ա Բ Գ Դ Ե Զ Է Ը Թ Ժ</td> <td><span data-sort-value="400 !">Early 5th Century</span> </td></tr> <tr> <td><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer numerals</a></td> <td>10</td> <td>០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩</td> <td><span data-sort-value="600 !">Early 7th Century</span> </td></tr> <tr> <td><a href="/wiki/Thai_numerals" title="Thai numerals">Thai numerals</a></td> <td>10</td> <td>๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙</td> <td><span data-sort-value="601 !">7th Century</span><sup id="cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200]_8-0" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200]-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad numerals</a></td> <td>10</td> <td>غ ظ ض ذ خ ث ت ش ر ق ص ف ع س ن م ل ك ي ط ح ز و هـ د ج ب ا</td> <td><span data-sort-value="680 !"><8th Century</span> </td></tr> <tr> <td><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese numerals</a> (financial)</td> <td>10</td> <td>零壹貳參肆伍陸柒捌玖拾佰仟萬億 (T. Chinese)<br />零壹贰叁肆伍陆柒捌玖拾佰仟萬億 (S. Chinese)</td> <td><span data-sort-value="690 !">late 7th/early 8th Century</span><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a></td> <td>10</td> <td>٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠</td> <td><span data-sort-value="701 !">8th Century</span> </td></tr> <tr> <td><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese numerals</a> (<a href="/wiki/Ch%E1%BB%AF_N%C3%B4m" title="Chữ Nôm">Chữ Nôm</a>)</td> <td>10</td> <td>𠬠𠄩𠀧𦊚𠄼𦒹𦉱𠔭𠃩</td> <td><span data-sort-value="799 !"><9th Century</span> </td></tr> <tr> <td><a href="/wiki/Western_Arabic_numerals" class="mw-redirect" title="Western Arabic numerals">Western Arabic numerals</a></td> <td>10</td> <td>0 1 2 3 4 5 6 7 8 9</td> <td><span data-sort-value="801 !">9th Century</span> </td></tr> <tr> <td><a href="/wiki/Glagolitic_numerals" title="Glagolitic numerals">Glagolitic numerals</a></td> <td>10</td> <td>Ⰰ Ⰱ Ⰲ Ⰳ Ⰴ Ⰵ Ⰶ Ⰷ Ⰸ ...</td> <td><span data-sort-value="800 !">9th Century</span> </td></tr> <tr> <td><a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic numerals</a></td> <td>10</td> <td>а в г д е ѕ з и ѳ і ...</td> <td><span data-sort-value="900 !">10th Century</span> </td></tr> <tr> <td><a href="/wiki/Rumi_Numeral_Symbols" title="Rumi Numeral Symbols">Rumi numerals</a></td> <td>10</td> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:Rumi_numerals_1-9.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Rumi_numerals_1-9.svg/150px-Rumi_numerals_1-9.svg.png" decoding="async" width="150" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Rumi_numerals_1-9.svg/225px-Rumi_numerals_1-9.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Rumi_numerals_1-9.svg/300px-Rumi_numerals_1-9.svg.png 2x" data-file-width="512" data-file-height="52" /></a><figcaption></figcaption></figure></td> <td><span data-sort-value="900 !">10th Century</span> </td></tr> <tr> <td><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese numerals</a></td> <td>10</td> <td>၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉</td> <td><span data-sort-value="1000 !">11th Century</span><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Tangut_numerals" title="Tangut numerals">Tangut numerals</a></td> <td>10</td> <td><style data-mw-deduplicate="TemplateStyles:r1065318431">.mw-parser-output .Tangut{font-family:"Tangut Yinchuan","Tangut N4694","New Tangut","New Tangut Std","Tangut TWU","TH-Tshyn-P1","TH-Feon-B","Noto Serif Tangut"}</style><span class="Tangut" style="display:inline-block; text-orientation: upright; -webkit-text-orientation: upright;" title="lew ny so lyr ngwy chhiw sha ar gy gha">𘈩 𗍫 𘕕 𗥃 𗏁 𗤁 𗒹 𘉋 𗢭 𗰗</span></td> <td><span data-sort-value="1036 !">11th Century (1036)</span> </td></tr> <tr> <td><a href="/wiki/Cistercian_numerals" title="Cistercian numerals">Cistercian numerals</a></td> <td>10</td> <td><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Cistercian_numerals.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cistercian_numerals.svg/170px-Cistercian_numerals.svg.png" decoding="async" width="170" height="42" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cistercian_numerals.svg/255px-Cistercian_numerals.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Cistercian_numerals.svg/340px-Cistercian_numerals.svg.png 2x" data-file-width="512" data-file-height="126" /></a></span></td> <td><span data-sort-value="1200 !">13th Century</span> </td></tr> <tr> <td><a href="/wiki/Maya_numerals" title="Maya numerals">Maya numerals</a></td> <td>5<span style="font-size:88%;">&</span>20</td> <td><span typeof="mw:File"><a href="/wiki/File:0_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/0_maia.svg/15px-0_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/0_maia.svg/23px-0_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/0_maia.svg/30px-0_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:1_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/1_maia.svg/15px-1_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/1_maia.svg/23px-1_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/1_maia.svg/30px-1_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:2_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/2_maia.svg/15px-2_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/2_maia.svg/23px-2_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/2_maia.svg/30px-2_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:3_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/3_maia.svg/15px-3_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/3_maia.svg/23px-3_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/3_maia.svg/30px-3_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:4_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/4_maia.svg/15px-4_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/4_maia.svg/23px-4_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/4_maia.svg/30px-4_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:5_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/5_maia.svg/15px-5_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/5_maia.svg/23px-5_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/5_maia.svg/30px-5_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:6_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/6_maia.svg/15px-6_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/6_maia.svg/23px-6_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/6_maia.svg/30px-6_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:7_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/7_maia.svg/15px-7_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/7_maia.svg/23px-7_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/7_maia.svg/30px-7_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:8_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/8_maia.svg/15px-8_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/8_maia.svg/23px-8_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/8_maia.svg/30px-8_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:9_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/9_maia.svg/15px-9_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/9_maia.svg/23px-9_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/9_maia.svg/30px-9_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:10_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/10_maia.svg/15px-10_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/10_maia.svg/23px-10_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/10_maia.svg/30px-10_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:11_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/11_maia.svg/15px-11_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/11_maia.svg/23px-11_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/11_maia.svg/30px-11_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:12_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/12_maia.svg/15px-12_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/12_maia.svg/23px-12_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/12_maia.svg/30px-12_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:13_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/13_maia.svg/15px-13_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/13_maia.svg/23px-13_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/13_maia.svg/30px-13_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:14_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/14_maia.svg/15px-14_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/14_maia.svg/23px-14_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/14_maia.svg/30px-14_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:15_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/15_maia.svg/15px-15_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/15_maia.svg/23px-15_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/15_maia.svg/30px-15_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:16_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/16_maia.svg/15px-16_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/16_maia.svg/23px-16_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/16_maia.svg/30px-16_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:17_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/17_maia.svg/15px-17_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/17_maia.svg/23px-17_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/17_maia.svg/30px-17_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:18_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/18_maia.svg/15px-18_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/18_maia.svg/23px-18_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/18_maia.svg/30px-18_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span> <span typeof="mw:File"><a href="/wiki/File:19_maia.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/19_maia.svg/15px-19_maia.svg.png" decoding="async" width="15" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/19_maia.svg/23px-19_maia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/19_maia.svg/30px-19_maia.svg.png 2x" data-file-width="50" data-file-height="40" /></a></span></td> <td><span data-sort-value="1400 !"><15th Century</span> </td></tr> <tr> <td><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca numerals</a></td> <td>20</td> <td><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Muisca_cyphers_acc_acosta_humboldt_zerda.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Muisca_cyphers_acc_acosta_humboldt_zerda.svg/330px-Muisca_cyphers_acc_acosta_humboldt_zerda.svg.png" decoding="async" width="330" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Muisca_cyphers_acc_acosta_humboldt_zerda.svg/495px-Muisca_cyphers_acc_acosta_humboldt_zerda.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Muisca_cyphers_acc_acosta_humboldt_zerda.svg/660px-Muisca_cyphers_acc_acosta_humboldt_zerda.svg.png 2x" data-file-width="973" data-file-height="389" /></a></span></td> <td><span data-sort-value="1399 !"><15th Century</span> </td></tr> <tr> <td><a href="/wiki/Korean_numerals" title="Korean numerals">Korean numerals</a> (<a href="/wiki/Hangul" title="Hangul">Hangul</a>)</td> <td>10</td> <td>영 일 이 삼 사 오 육 칠 팔 구</td> <td><span data-sort-value="1443 !">15th Century (1443)</span> </td></tr> <tr> <td><a href="/wiki/Aztec_numerals" class="mw-redirect" title="Aztec numerals">Aztec numerals</a></td> <td>20</td> <td></td> <td><span data-sort-value="1500 !">16th Century</span> </td></tr> <tr> <td><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala numerals</a></td> <td>10</td> <td>෦ ෧ ෨ ෩ ෪ ෫ ෬ ෭ ෮ ෯ 𑇡 𑇢 𑇣<br />𑇤 𑇥 𑇦 𑇧 𑇨 𑇩 𑇪 𑇫 𑇬 𑇭 𑇮 𑇯 𑇰 𑇱 𑇲 𑇳 𑇴</td> <td><span data-sort-value="1699 !"><18th Century</span> </td></tr> <tr> <td><a href="/wiki/Pentadic_numerals" title="Pentadic numerals">Pentadic runes</a></td> <td>10</td> <td><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Pentimal_Runes_1_through_10.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Pentimal_Runes_1_through_10.svg/170px-Pentimal_Runes_1_through_10.svg.png" decoding="async" width="170" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Pentimal_Runes_1_through_10.svg/255px-Pentimal_Runes_1_through_10.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Pentimal_Runes_1_through_10.svg/340px-Pentimal_Runes_1_through_10.svg.png 2x" data-file-width="361" data-file-height="41" /></a></span></td> <td><span data-sort-value="1800 !">19th Century</span> </td></tr> <tr> <td><a href="/wiki/Cherokee_syllabary#Numerals" title="Cherokee syllabary">Cherokee numerals</a></td> <td>10</td> <td><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Cherokee_Numbers_%E2%80%93_cropped_(1-20).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png/440px-Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png" decoding="async" width="440" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png/660px-Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png/880px-Cherokee_Numbers_%E2%80%93_cropped_%281-20%29.png 2x" data-file-width="1502" data-file-height="134" /></a></span></td> <td><span data-sort-value="1820 !">19th Century (1820s)</span> </td></tr> <tr> <td><a href="/wiki/Vai_syllabary#Digits" title="Vai syllabary">Vai numerals</a></td> <td>10</td> <td>꘠ ꘡ ꘢ ꘣ ꘤ ꘥ ꘦ ꘧ ꘨ ꘩ <sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1832 !">19th Century (1832)<sup id="cite_ref-Open_Science_Framework_12-0" class="reference"><a href="#cite_note-Open_Science_Framework-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Bamum_script#Numbers" title="Bamum script">Bamum numerals</a></td> <td>10</td> <td>ꛯ ꛦ ꛧ ꛨ ꛩ ꛪ ꛫ ꛬ ꛭ ꛮ <sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1896 !">19th Century (1896)<sup id="cite_ref-Open_Science_Framework_12-1" class="reference"><a href="#cite_note-Open_Science_Framework-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Mende_Kikakui_script" title="Mende Kikakui script">Mende Kikakui numerals</a></td> <td>10</td> <td>𞣏 𞣎 𞣍 𞣌 𞣋 𞣊 𞣉 𞣈 𞣇 <sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1896 !">20th Century (1917)<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Osmanya_script" class="mw-redirect" title="Osmanya script">Osmanya numerals</a></td> <td>10</td> <td>𐒠 𐒡 𐒢 𐒣 𐒤 𐒥 𐒦 𐒧 𐒨 𐒩</td> <td><span data-sort-value="1921 !">20th Century (1920s)</span> </td></tr> <tr> <td><a href="/wiki/Medefaidrin#Numbers_and_dates" title="Medefaidrin">Medefaidrin numerals</a></td> <td>20</td> <td>𖺀 𖺁/𖺔 𖺂/𖺕 𖺃/𖺖 𖺄 𖺅 𖺆 𖺇 𖺈 𖺉 𖺊 𖺋 𖺌 𖺍 𖺎 𖺏 𖺐 𖺑 𖺒 𖺓 <sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1930 !">20th Century (1930s)<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/N%27Ko_script#Numerals" title="N'Ko script">N'Ko numerals</a></td> <td>10</td> <td>߉ ߈ ߇ ߆ ߅ ߄ ߃ ߂ ߁ ߀ <sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1949 !">20th Century (1949)<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Pahawh_Hmong#Numeral_system" title="Pahawh Hmong">Hmong numerals</a></td> <td>10</td> <td><style data-mw-deduplicate="TemplateStyles:r1009642731">.mw-parser-output .script-Hmng{font-family:"Noto Sans Pahawh Hmong"}</style><span class="script-Hmng">𖭐</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭑</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭒</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭓</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭔</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭕</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭖</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭗</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭘</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1009642731"><span class="script-Hmng">𖭑𖭐</span></td> <td><span data-sort-value="1959 !">20th Century (1959)</span> </td></tr> <tr> <td><a href="/wiki/Garay_alphabet#Numbers" title="Garay alphabet">Garay numerals</a></td> <td>10</td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Garay_numbers.png" class="mw-file-description" title="Garay numbers"><img alt="Garay numbers" src="//upload.wikimedia.org/wikipedia/commons/2/25/Garay_numbers.png" decoding="async" width="354" height="72" class="mw-file-element" data-file-width="354" data-file-height="72" /></a></span><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1961 !">20th Century (1961)<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Adlam_script#Digits" title="Adlam script">Adlam numerals</a></td> <td>10</td> <td>𞥙 𞥘 𞥗 𞥖 𞥕 𞥔 𞥓 𞥒 𞥑 𞥐 <sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1989 !">20th Century (1989)<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik numerals</a></td> <td>5<span style="font-size:88%;">&</span>20</td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_0.svg" class="mw-file-description" title="𝋀"><img alt="𝋀" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Kaktovik_digit_0.svg/10px-Kaktovik_digit_0.svg.png" decoding="async" width="10" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Kaktovik_digit_0.svg/15px-Kaktovik_digit_0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Kaktovik_digit_0.svg/20px-Kaktovik_digit_0.svg.png 2x" data-file-width="22" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_1.svg" class="mw-file-description" title="𝋁"><img alt="𝋁" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Kaktovik_digit_1.svg/10px-Kaktovik_digit_1.svg.png" decoding="async" width="10" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Kaktovik_digit_1.svg/15px-Kaktovik_digit_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Kaktovik_digit_1.svg/20px-Kaktovik_digit_1.svg.png 2x" data-file-width="22" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_2.svg" class="mw-file-description" title="𝋂"><img alt="𝋂" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Kaktovik_digit_2.svg/14px-Kaktovik_digit_2.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Kaktovik_digit_2.svg/22px-Kaktovik_digit_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Kaktovik_digit_2.svg/29px-Kaktovik_digit_2.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_3.svg" class="mw-file-description" title="𝋃"><img alt="𝋃" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Kaktovik_digit_3.svg/14px-Kaktovik_digit_3.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Kaktovik_digit_3.svg/21px-Kaktovik_digit_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Kaktovik_digit_3.svg/28px-Kaktovik_digit_3.svg.png 2x" data-file-width="31" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_4.svg" class="mw-file-description" title="𝋄"><img alt="𝋄" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Kaktovik_digit_4.svg/15px-Kaktovik_digit_4.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Kaktovik_digit_4.svg/22px-Kaktovik_digit_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Kaktovik_digit_4.svg/30px-Kaktovik_digit_4.svg.png 2x" data-file-width="33" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_5.svg" class="mw-file-description" title="𝋅"><img alt="𝋅" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Kaktovik_digit_5.svg/13px-Kaktovik_digit_5.svg.png" decoding="async" width="13" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Kaktovik_digit_5.svg/20px-Kaktovik_digit_5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Kaktovik_digit_5.svg/27px-Kaktovik_digit_5.svg.png 2x" data-file-width="30" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_6.svg" class="mw-file-description" title="𝋆"><img alt="𝋆" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Kaktovik_digit_6.svg/15px-Kaktovik_digit_6.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Kaktovik_digit_6.svg/22px-Kaktovik_digit_6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Kaktovik_digit_6.svg/30px-Kaktovik_digit_6.svg.png 2x" data-file-width="33" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_7.svg" class="mw-file-description" title="𝋇"><img alt="𝋇" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Kaktovik_digit_7.svg/15px-Kaktovik_digit_7.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Kaktovik_digit_7.svg/22px-Kaktovik_digit_7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Kaktovik_digit_7.svg/30px-Kaktovik_digit_7.svg.png 2x" data-file-width="33" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_8.svg" class="mw-file-description" title="𝋈"><img alt="𝋈" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Kaktovik_digit_8.svg/14px-Kaktovik_digit_8.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Kaktovik_digit_8.svg/22px-Kaktovik_digit_8.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Kaktovik_digit_8.svg/29px-Kaktovik_digit_8.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_9.svg" class="mw-file-description" title="𝋉"><img alt="𝋉" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Kaktovik_digit_9.svg/14px-Kaktovik_digit_9.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Kaktovik_digit_9.svg/22px-Kaktovik_digit_9.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Kaktovik_digit_9.svg/29px-Kaktovik_digit_9.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_10.svg" class="mw-file-description" title="𝋊"><img alt="𝋊" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Kaktovik_digit_10.svg/14px-Kaktovik_digit_10.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Kaktovik_digit_10.svg/21px-Kaktovik_digit_10.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Kaktovik_digit_10.svg/28px-Kaktovik_digit_10.svg.png 2x" data-file-width="31" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_11.svg" class="mw-file-description" title="𝋋"><img alt="𝋋" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Kaktovik_digit_11.svg/15px-Kaktovik_digit_11.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Kaktovik_digit_11.svg/22px-Kaktovik_digit_11.svg.png 1.5x, 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src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Kaktovik_digit_13.svg/14px-Kaktovik_digit_13.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Kaktovik_digit_13.svg/22px-Kaktovik_digit_13.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Kaktovik_digit_13.svg/29px-Kaktovik_digit_13.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_14.svg" class="mw-file-description" title="𝋎"><img alt="𝋎" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Kaktovik_digit_14.svg/14px-Kaktovik_digit_14.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Kaktovik_digit_14.svg/22px-Kaktovik_digit_14.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Kaktovik_digit_14.svg/29px-Kaktovik_digit_14.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_15.svg" class="mw-file-description" title="𝋏"><img alt="𝋏" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Kaktovik_digit_15.svg/14px-Kaktovik_digit_15.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Kaktovik_digit_15.svg/22px-Kaktovik_digit_15.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Kaktovik_digit_15.svg/29px-Kaktovik_digit_15.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_16.svg" class="mw-file-description" title="𝋐"><img alt="𝋐" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kaktovik_digit_16.svg/15px-Kaktovik_digit_16.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kaktovik_digit_16.svg/23px-Kaktovik_digit_16.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Kaktovik_digit_16.svg/31px-Kaktovik_digit_16.svg.png 2x" data-file-width="34" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_17.svg" class="mw-file-description" title="𝋑"><img alt="𝋑" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kaktovik_digit_17.svg/15px-Kaktovik_digit_17.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kaktovik_digit_17.svg/23px-Kaktovik_digit_17.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kaktovik_digit_17.svg/31px-Kaktovik_digit_17.svg.png 2x" data-file-width="34" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_18.svg" class="mw-file-description" title="𝋒"><img alt="𝋒" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kaktovik_digit_18.svg/14px-Kaktovik_digit_18.svg.png" decoding="async" width="14" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kaktovik_digit_18.svg/22px-Kaktovik_digit_18.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kaktovik_digit_18.svg/29px-Kaktovik_digit_18.svg.png 2x" data-file-width="32" data-file-height="53" /></a></span> <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Kaktovik_digit_19.svg" class="mw-file-description" title="𝋓"><img alt="𝋓" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Kaktovik_digit_19.svg/15px-Kaktovik_digit_19.svg.png" decoding="async" width="15" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Kaktovik_digit_19.svg/22px-Kaktovik_digit_19.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Kaktovik_digit_19.svg/30px-Kaktovik_digit_19.svg.png 2x" data-file-width="33" data-file-height="53" /></a></span> <br /> 𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 <sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></td> <td><span data-sort-value="1994 !">20th Century (1994)<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></span> </td></tr> <tr> <td><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese numerals</a> </td> <td>10 </td> <td>᮰ ᮱ ᮲ ᮳ ᮴ ᮵ ᮶ ᮷ ᮸ ᮹ </td> <td>20th Century (1996)<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="By_type_of_notation">By type of notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=2" title="Edit section: By type of notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Positional_numeral_systems"></span> Numeral systems are classified here as to whether they use <a href="/wiki/Positional_notation" title="Positional notation">positional notation</a> (also known as place-value notation), and further categorized by <a href="/wiki/Radix" title="Radix">radix</a> or base. </p> <div class="mw-heading mw-heading3"><h3 id="Standard_positional_numeral_systems">Standard positional numeral systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=3" title="Edit section: Standard positional numeral systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreliable_sources plainlinks metadata ambox ambox-content ambox-unreliable_sources" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Text_document_with_red_question_mark.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Some of this article's <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">listed sources</a> <b>may not be <a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliable</a></b>.<span class="hide-when-compact"> Please help improve this article by looking for better, more reliable sources. Unreliable citations may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">April 2023</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Binary_clock.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/220px-Binary_clock.svg.png" decoding="async" width="220" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/330px-Binary_clock.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/440px-Binary_clock.svg.png 2x" data-file-width="539" data-file-height="395" /></a><figcaption>A <a href="/wiki/Binary_clock" title="Binary clock">binary clock</a> might use <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">LEDs</a> to express binary values. In this clock, each column of LEDs shows a <a href="/wiki/Binary-coded_decimal" title="Binary-coded decimal">binary-coded decimal</a> numeral of the traditional <a href="/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a> time.</figcaption></figure> <p>The common names are derived <a href="/wiki/Hexadecimal#Etymology" title="Hexadecimal">somewhat arbitrarily</a> from a mix of <a href="/wiki/Latin" title="Latin">Latin</a> and <a href="/wiki/Greek_language" title="Greek language">Greek</a>, in some cases including roots from both languages within a single name.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> There have been some proposals for standardisation.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td>2</td> <td><a href="/wiki/Binary_number" title="Binary number">Binary</a></td> <td><a href="/wiki/Digital_signal" title="Digital signal">Digital</a> <a href="/wiki/Computing" title="Computing">computing</a>, <a href="/wiki/Imperial_units" title="Imperial units">imperial</a> and <a href="/wiki/United_States_customary_units" title="United States customary units">customary</a> <a href="/wiki/Volume" title="Volume">volume</a> (<a href="/wiki/Bushel" title="Bushel">bushel</a>-<a href="/wiki/Kenning_(unit)" class="mw-redirect" title="Kenning (unit)">kenning</a>-<a href="/wiki/Peck" title="Peck">peck</a>-<a href="/wiki/Gallon" title="Gallon">gallon</a>-<a href="/wiki/English_units#Volume" title="English units">pottle</a>-<a href="/wiki/Quart" title="Quart">quart</a>-<a href="/wiki/Pint" title="Pint">pint</a>-<a href="/wiki/Cup_(unit)" title="Cup (unit)">cup</a>-<a href="/wiki/Gill_(volume)" class="mw-redirect" title="Gill (volume)">gill</a>-<a href="/wiki/English_units#Volume" title="English units">jack</a>-<a href="/wiki/Fluid_ounce" title="Fluid ounce">fluid ounce</a>-<a href="/wiki/Tablespoon" title="Tablespoon">tablespoon</a>) </td></tr> <tr> <td>3</td> <td><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">Ternary</a>, trinary<sup id="cite_ref-Kindra2022_29-0" class="reference"><a href="#cite_note-Kindra2022-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></td> <td><a href="/wiki/Cantor_set" title="Cantor set">Cantor set</a> (all points in [0,1] that <i>can</i> be represented in ternary with no 1s); <a href="/wiki/Counting" title="Counting">counting</a> <a href="/wiki/Tasbih" title="Tasbih">Tasbih</a> in <a href="/wiki/Islam" title="Islam">Islam</a>; <a href="/wiki/Hand_(unit)" title="Hand (unit)">hand</a>-<a href="/wiki/Foot_(unit)" title="Foot (unit)">foot</a>-<a href="/wiki/Yard" title="Yard">yard</a> and teaspoon-tablespoon-shot <a href="/wiki/Measurement_system" class="mw-redirect" title="Measurement system">measurement systems</a>; most <i><a href="/wiki/Radix_economy" class="mw-redirect" title="Radix economy">economical</a></i> integer base </td></tr> <tr> <td>4</td> <td><a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">Quaternary</a></td> <td><a href="/wiki/Chumashan_languages" title="Chumashan languages">Chumashan languages</a> and <a href="/wiki/Kharosthi#Numerals" title="Kharosthi">Kharosthi numerals</a> </td></tr> <tr> <td>5</td> <td><a href="/wiki/Quinary" title="Quinary">Quinary</a></td> <td><a href="/wiki/Gumatj_language" class="mw-redirect" title="Gumatj language">Gumatj</a>, <a href="/wiki/Ateso_language" class="mw-redirect" title="Ateso language">Ateso</a>, <a href="/wiki/Nunggubuyu_language" title="Nunggubuyu language">Nunggubuyu</a>, <a href="/wiki/Kuurn_Kopan_Noot_language" class="mw-redirect" title="Kuurn Kopan Noot language">Kuurn Kopan Noot</a>, and <a href="/wiki/Saraveca_language" title="Saraveca language">Saraveca</a> languages; common count grouping e.g. <a href="/wiki/Tally_marks" title="Tally marks">tally marks</a> </td></tr> <tr> <td>6</td> <td><a href="/wiki/Senary" title="Senary">Senary</a>, <a href="/wiki/Seximal" class="mw-redirect" title="Seximal">seximal</a></td> <td><a href="/wiki/Diceware" title="Diceware">Diceware</a>, <a href="/wiki/Ndom_language" title="Ndom language">Ndom</a>, <a href="/wiki/Kanum_language" class="mw-redirect" title="Kanum language">Kanum</a>, and <a href="/wiki/Proto-Uralic_language" title="Proto-Uralic language">Proto-Uralic language</a> (suspected) </td></tr> <tr> <td>7</td> <td>Septimal, <a href="/wiki/Septenary" class="mw-redirect" title="Septenary">Septenary</a><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></td> <td><a href="/wiki/Week" title="Week">Weeks</a> timekeeping, Western music <a href="/wiki/Letter_notation" title="Letter notation">letter notation</a> </td></tr> <tr> <td>8</td> <td><a href="/wiki/Octal" title="Octal">Octal</a></td> <td><a href="/wiki/Charles_XII_of_Sweden#Scientific_contributions" title="Charles XII of Sweden">Charles XII of Sweden</a>, <a href="/wiki/Filesystem_permissions#Octal_notation" class="mw-redirect" title="Filesystem permissions">Unix-like permissions</a>, <a href="/wiki/Transponder_(aeronautics)" title="Transponder (aeronautics)">Squawk codes</a>, <a href="/wiki/PDP-11_architecture#Memory_management" title="PDP-11 architecture">DEC PDP-11</a>, <a href="/wiki/Yuki_language" title="Yuki language">Yuki</a>, <a href="/wiki/Pame_languages" title="Pame languages">Pame</a>, compact notation for binary numbers, Xiantian (<a href="/wiki/I_Ching" title="I Ching">I Ching</a>, China) </td></tr> <tr> <td>9</td> <td><a href="/wiki/Nonary" class="mw-redirect" title="Nonary">Nonary</a>, <a href="/wiki/Nonal" class="mw-redirect" title="Nonal">nonal</a></td> <td>Compact notation for <a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">ternary</a> </td></tr> <tr> <td>10</td> <td><a href="/wiki/Decimal" title="Decimal">Decimal</a>, denary</td> <td>Most widely used by contemporary societies<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>11</td> <td><a href="/wiki/Undecimal" title="Undecimal">Undecimal</a>, unodecimal, undenary</td> <td>A base-11 number system was attributed to the <a href="/wiki/M%C4%81ori_people" title="Māori people">Māori</a> (<a href="/wiki/New_Zealand" title="New Zealand">New Zealand</a>) in the 19th century<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Pangwa" class="mw-redirect" title="Pangwa">Pangwa</a> (<a href="/wiki/Tanzania" title="Tanzania">Tanzania</a>) in the 20th century.<sup id="cite_ref-THOMAS_35-0" class="reference"><a href="#cite_note-THOMAS-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Briefly proposed during the <a href="/wiki/French_Revolution" title="French Revolution">French Revolution</a> to settle a dispute between those proposing a shift to duodecimal and those who were content with decimal. Used as a <a href="/wiki/International_Standard_Book_Number#Check_digits" class="mw-redirect" title="International Standard Book Number">check digit in ISBN</a> for 10-digit ISBNs. Applications in computer science and technology.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Featured in popular fiction. </td></tr> <tr> <td>12</td> <td><a href="/wiki/Duodecimal" title="Duodecimal">Duodecimal</a>, dozenal</td> <td>Languages in the <a href="/wiki/Nigeria" title="Nigeria">Nigerian</a> Middle Belt <a href="/wiki/Janji_language" title="Janji language">Janji</a>, <a href="/wiki/Gbiri-Niragu_language" title="Gbiri-Niragu language">Gbiri-Niragu</a>, <a href="/wiki/Piti_language" title="Piti language">Piti</a>, and the Nimbia dialect of <a href="/wiki/Gwandara_language" title="Gwandara language">Gwandara</a>; <a href="/wiki/Chepang_language" title="Chepang language">Chepang language</a> of <a href="/wiki/Nepal" title="Nepal">Nepal</a>, and the Mahl dialect of <a href="/wiki/Maldivian_language" title="Maldivian language">Maldivian</a>; <a href="/wiki/Dozen" title="Dozen">dozen</a>-<a href="/wiki/Gross_(unit)" title="Gross (unit)">gross</a>-great gross counting; <a href="/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a> and <a href="/wiki/Month" title="Month">months</a> timekeeping; years of <a href="/wiki/Chinese_zodiac" title="Chinese zodiac">Chinese zodiac</a>; <a href="/wiki/Foot_(unit)" title="Foot (unit)">foot</a> and <a href="/wiki/Inch" title="Inch">inch</a>; <a href="/wiki/Roman_numerals#Fractions" title="Roman numerals">Roman fractions</a>; <a href="/wiki/Penny" title="Penny">penny</a> and <a href="/wiki/Shilling" title="Shilling">shilling</a> </td></tr> <tr> <td>13</td> <td>Tredecimal, tridecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201213_39-0" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201213-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-0" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td><a href="/wiki/Conway_base_13_function" title="Conway base 13 function">Conway base 13 function</a>. </td></tr> <tr> <td>14</td> <td>Quattuordecimal, quadrodecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201213_39-1" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201213-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-1" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td>Programming for the <a href="/wiki/Hewlett-Packard" title="Hewlett-Packard">HP</a> 9100A/B calculator<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> and image processing applications;<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pound_(mass)" title="Pound (mass)">pound</a> and <a href="/wiki/Stone_(mass)" class="mw-redirect" title="Stone (mass)">stone</a>. </td></tr> <tr> <td>15</td> <td>Quindecimal, pentadecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201214_43-0" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201214-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-2" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td>Telephony routing over IP, and the <a href="/wiki/Huli_language" title="Huli language">Huli language</a>. </td></tr> <tr> <td>16</td> <td><a href="/wiki/Hexadecimal" title="Hexadecimal">Hexadecimal</a>, sexadecimal, sedecimal </td> <td>Compact notation for <a href="/wiki/Binary_data" title="Binary data">binary data</a>; <a href="/wiki/Tonal_system" title="Tonal system">tonal system</a>; <a href="/wiki/Ounce" title="Ounce">ounce</a> and <a href="/wiki/Pound_(mass)" title="Pound (mass)">pound</a>. </td></tr> <tr> <td>17</td> <td>Septendecimal, heptadecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201214_43-1" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201214-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-3" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td> </td></tr> <tr> <td>18</td> <td>Octodecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201214_43-2" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201214-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-4" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td>A base in which 7<sup>n</sup> is <a href="/wiki/Palindromic_number" title="Palindromic number">palindromic</a> for n = 3, 4, 6, 9. </td></tr> <tr> <td><a href="/wiki/19_(number)" title="19 (number)">19</a></td> <td>Undevicesimal, nonadecimal<sup id="cite_ref-FOOTNOTEDasLanjewar201214_43-3" class="reference"><a href="#cite_note-FOOTNOTEDasLanjewar201214-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTERawatSah2013_40-5" class="reference"><a href="#cite_note-FOOTNOTERawatSah2013-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></td> <td>Used as a basis for the <a href="/wiki/Bah%C3%A1%27%C3%AD_calendar" class="mw-redirect" title="Bahá'í calendar">Bahá'í calendar</a>. </td></tr> <tr> <td>20</td> <td><a href="/wiki/Vigesimal" title="Vigesimal">Vigesimal</a></td> <td><a href="/wiki/Basque_language" title="Basque language">Basque</a>, <a href="/wiki/Yan_Tan_Tethera" class="mw-redirect" title="Yan Tan Tethera">Celtic</a>, <a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a>, <a href="/wiki/Inuit_numerals" class="mw-redirect" title="Inuit numerals">Inuit</a>, <a href="/wiki/Yoruba_numerals" title="Yoruba numerals">Yoruba</a>, <a href="/wiki/Tlingit_people" class="mw-redirect" title="Tlingit people">Tlingit</a>, and <a href="/wiki/Dzongkha_numerals" title="Dzongkha numerals">Dzongkha</a> numerals; <a href="/wiki/Santali_language" title="Santali language">Santali</a>, and <a href="/wiki/Ainu_language" title="Ainu language">Ainu</a> languages; <a href="/wiki/Shilling" title="Shilling">shilling</a> and <a href="/wiki/Pound_(currency)" title="Pound (currency)">pound</a> </td></tr> <tr> <td>5&20</td> <td><a href="/wiki/Quinary" title="Quinary">Quinary</a>-<a href="/wiki/Vigesimal" title="Vigesimal">vigesimal</a><sup id="cite_ref-Nykl_44-0" class="reference"><a href="#cite_note-Nykl-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200:]_"The_early_origin_of_bar-and-dot_numeration_alongside_the_Middle_Formative_Mesoamerican_scripts,_the_quinary-vigesimal_structure_of_the_system,_and_the_general_increase_in_the_frequency_and_complexity_of_numeral_expressions_over_time_all_point_to_its_indigenous_development."_46-0" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200:]_"The_early_origin_of_bar-and-dot_numeration_alongside_the_Middle_Formative_Mesoamerican_scripts,_the_quinary-vigesimal_structure_of_the_system,_and_the_general_increase_in_the_frequency_and_complexity_of_numeral_expressions_over_time_all_point_to_its_indigenous_development."-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup></td> <td><a href="/wiki/Greenlandic_language" title="Greenlandic language">Greenlandic</a>, <a href="/wiki/I%C3%B1upiaq_language#Numerals" title="Iñupiaq language">Iñupiaq</a>, <a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik</a>, <a href="/wiki/Maya_numerals" title="Maya numerals">Maya</a>, <a href="/wiki/Nunivak_Cup%CA%BCig_language" title="Nunivak Cupʼig language">Nunivak Cupʼig</a>, and <a href="/wiki/Central_Alaskan_Yup%CA%BCik" title="Central Alaskan Yupʼik">Yupʼik</a> numerals – "wide-spread... in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon"<sup id="cite_ref-Nykl_44-1" class="reference"><a href="#cite_note-Nykl-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>21</td> <td></td> <td>The smallest base in which all fractions <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">18</span></span>⁠</span> have <a href="/wiki/Repeating_decimal" title="Repeating decimal">periods</a> of 4 or shorter. </td></tr> <tr> <td>23</td> <td></td> <td><a href="/wiki/Kalam_language" title="Kalam language">Kalam language</a>,<sup id="cite_ref-Laycock_1975_219–233_47-0" class="reference"><a href="#cite_note-Laycock_1975_219–233-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Kobon_language" title="Kobon language">Kobon language</a><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="No mention in linked articles, and I only found a few loose mentions; please check if base 23 was actually used in these languages. (September 2019)">citation needed</span></a></i>]</sup> </td></tr> <tr> <td>24</td> <td><a href="https://en.wiktionary.org/wiki/quadravigesimal" class="extiw" title="wikt:quadravigesimal">Quadravigesimal</a><sup id="cite_ref-Dibbell_48-0" class="reference"><a href="#cite_note-Dibbell-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup></td> <td><a href="/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a> timekeeping; <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a>; <a href="/wiki/Kaugel_language" title="Kaugel language">Kaugel language</a>. </td></tr> <tr> <td>25</td> <td></td> <td>Sometimes used as compact notation for quinary. </td></tr> <tr> <td>26</td> <td><a href="https://en.wiktionary.org/wiki/hexavigesimal" class="extiw" title="wikt:hexavigesimal">Hexavigesimal</a><sup id="cite_ref-Dibbell_48-1" class="reference"><a href="#cite_note-Dibbell-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></td> <td>Sometimes used for encryption or ciphering,<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> using all letters in the <a href="/wiki/English_alphabet" title="English alphabet">English alphabet</a> </td></tr> <tr> <td>27</td> <td>Septemvigesimal</td> <td><a href="/wiki/Telefol_language" title="Telefol language">Telefol</a>,<sup id="cite_ref-Laycock_1975_219–233_47-1" class="reference"><a href="#cite_note-Laycock_1975_219–233-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Oksapmin_language" title="Oksapmin language">Oksapmin</a>,<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Wambon_language" title="Wambon language">Wambon</a>,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Hewa_language" title="Hewa language">Hewa</a><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> languages. Mapping the nonzero digits to the alphabet and zero to the space is occasionally used to provide <a href="/wiki/Checksum" title="Checksum">checksums</a> for alphabetic data such as personal names,<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> to provide a concise encoding of alphabetic strings,<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> or as the basis for a form of <a href="/wiki/Gematria" title="Gematria">gematria</a>.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> Compact notation for <a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">ternary</a>. </td></tr> <tr> <td>28</td> <td></td> <td>Months timekeeping. </td></tr> <tr> <td>30</td> <td>Trigesimal</td> <td>The <a href="/wiki/Natural_Area_Code" title="Natural Area Code">Natural Area Code</a>, this is the smallest base such that all of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">6</span></span>⁠</span> terminate, a number n is a <a href="/wiki/Regular_number" title="Regular number">regular number</a> if and only if <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">n</span></span>⁠</span> terminates in base 30. </td></tr> <tr> <td><a href="/wiki/Base_32" class="mw-redirect" title="Base 32">32</a></td> <td><a href="/wiki/Base32" title="Base32">Duotrigesimal</a></td> <td>Found in the <a href="/wiki/Ngiti_language" title="Ngiti language">Ngiti language</a>. </td></tr> <tr> <td>33</td> <td></td> <td>Use of letters (except I, O, Q) with digits in <a href="/wiki/Vehicle_registration_plates_of_Hong_Kong" title="Vehicle registration plates of Hong Kong">vehicle registration plates of Hong Kong</a>. </td></tr> <tr> <td>34</td> <td></td> <td>Using all numbers and all letters except I and O; the smallest base where <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> terminates and all of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">18</span></span>⁠</span> have periods of 4 or shorter. </td></tr> <tr> <td>35</td> <td></td> <td>Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O. </td></tr> <tr> <td><a href="/wiki/Base_36" class="mw-redirect" title="Base 36">36</a></td> <td><a href="https://en.wiktionary.org/wiki/hexatrigesimal" class="extiw" title="wikt:hexatrigesimal">Hexatrigesimal</a><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup></td> <td>Covers the ten decimal digits and all letters of the <a href="/wiki/English_alphabet" title="English alphabet">English alphabet</a>. </td></tr> <tr> <td>37</td> <td></td> <td>Covers the ten decimal digits and all letters of the <a href="/wiki/Spanish_alphabet" class="mw-redirect" title="Spanish alphabet">Spanish alphabet</a>. </td></tr> <tr> <td>38</td> <td></td> <td>Covers the <a href="/wiki/Duodecimal" title="Duodecimal">duodecimal</a> digits and all letters of the English alphabet. </td></tr> <tr> <td>40</td> <td>Quadragesimal</td> <td><a href="/wiki/DEC_RADIX_50" title="DEC RADIX 50">DEC RADIX 50</a>/<a href="/wiki/DEC_MOD40" class="mw-redirect" title="DEC MOD40">MOD40</a> encoding used to compactly represent file names and other symbols on <a href="/wiki/Digital_Equipment_Corporation" title="Digital Equipment Corporation">Digital Equipment Corporation</a> computers. The character set is a subset of ASCII consisting of space, upper case letters, the punctuation marks "$", ".", and "%", and the numerals. </td></tr> <tr> <td>42</td> <td></td> <td>Largest base for which all <a href="/wiki/Minimal_prime_(recreational_mathematics)" title="Minimal prime (recreational mathematics)">minimal primes</a> are known. </td></tr> <tr> <td>47</td> <td></td> <td>Smallest base for which no <a href="/wiki/Generalized_Wieferich_prime" class="mw-redirect" title="Generalized Wieferich prime">generalized Wieferich primes</a> are known. </td></tr> <tr> <td>49</td> <td></td> <td>Compact notation for septenary. </td></tr> <tr> <td>50</td> <td>Quinquagesimal</td> <td><a href="/wiki/SQUOZE" title="SQUOZE">SQUOZE</a> encoding used to compactly represent file names and other symbols on some <a href="/wiki/IBM" title="IBM">IBM</a> computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits. </td></tr> <tr> <td>52</td> <td></td> <td>Covers the digits and letters assigned to base 62 apart from the basic vowel letters;<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> similar to base 26 but distinguishing upper- and lower-case letters. </td></tr> <tr> <td>56</td> <td></td> <td>A variant of base 58.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (August 2023)">clarification needed</span></a></i>]</sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>57</td> <td></td> <td>Covers base 62 apart from I, O, l, U, and u,<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> or I, 1, l, 0, and O.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>58</td> <td></td> <td>Covers base 62 apart from 0 (zero), I (capital i), O (capital o) and l (lower case L).<sup id="cite_ref-base58_63-0" class="reference"><a href="#cite_note-base58-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>60</td> <td><a href="/wiki/Sexagesimal" title="Sexagesimal">Sexagesimal</a></td> <td><a href="/wiki/Babylonian_numerals" class="mw-redirect" title="Babylonian numerals">Babylonian numerals</a> and <a href="/wiki/Sumerian_language" title="Sumerian language">Sumerian</a>; <a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a>-<a href="/wiki/Minute_and_second_of_arc" title="Minute and second of arc">minutes-seconds</a> and <a href="/wiki/Hour" title="Hour">hours</a>-<a href="/wiki/Minute" title="Minute">minutes</a>-<a href="/wiki/Second" title="Second">seconds</a> measurement systems; <a href="/wiki/Ekari_language" title="Ekari language">Ekari</a>; covers base 62 apart from I, O, and l, but including _(underscore).<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Base62" title="Base62">62</a></td> <td></td> <td>Can be notated with the digits 0–9 and the cased letters A–Z and a–z of the English alphabet. </td></tr> <tr> <td><a href="/wiki/Base64" title="Base64">64</a></td> <td>Tetrasexagesimal</td> <td><a href="/wiki/I_Ching" title="I Ching">I Ching</a> in China.<br />This system is conveniently coded into <a href="/wiki/ASCII" title="ASCII">ASCII</a> by using the 26 letters of the Latin alphabet in both upper and lower case (52 total) plus 10 numerals (62 total) and then adding two special characters (+ and /). </td></tr> <tr> <td>72</td> <td></td> <td>The smallest base greater than binary such that no three-digit <a href="/wiki/Narcissistic_number" title="Narcissistic number">narcissistic number</a> exists. </td></tr> <tr> <td>80</td> <td>Octogesimal</td> <td>Used as a sub-base in <a href="/wiki/Supyire_language" title="Supyire language">Supyire</a>. </td></tr> <tr> <td>85</td> <td></td> <td><a href="/wiki/Ascii85" title="Ascii85">Ascii85</a> encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85<sup>5</sup> is only slightly bigger than 2<sup>32</sup>. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. </td></tr> <tr> <td>89</td> <td></td> <td>Largest base for which all <a href="/wiki/Left-truncatable_prime" class="mw-redirect" title="Left-truncatable prime">left-truncatable primes</a> are known. </td></tr> <tr> <td>90</td> <td>Nonagesimal</td> <td>Related to <a href="/wiki/Goormaghtigh_conjecture" title="Goormaghtigh conjecture">Goormaghtigh conjecture</a> for the generalized <a href="/wiki/Repunit" title="Repunit">repunit</a> numbers (111 in base 90 = 1111111111111 in base 2). </td></tr> <tr> <td>95</td> <td></td> <td>Number of <abbr title="incl. the dubiously printable 0x20 space character, which is technically considered part of the set of printable ASCII characters">printable</abbr> ASCII characters.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>96</td> <td></td> <td>Total number of character codes in the (six) <a href="/wiki/ASCII_stick" class="mw-redirect" title="ASCII stick">ASCII sticks</a> containing printable characters. </td></tr> <tr> <td>97</td> <td></td> <td>Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized <a href="/wiki/Wagstaff_prime" title="Wagstaff prime">Wagstaff primes</a> are known. </td></tr> <tr> <td>100</td> <td>Centesimal</td> <td>As 100=10<sup>2</sup>, these are two decimal digits. </td></tr> <tr> <td>121</td> <td></td> <td>Number expressible with two undecimal digits. </td></tr> <tr> <td>125</td> <td></td> <td>Number expressible with three quinary digits. </td></tr> <tr> <td>128</td> <td></td> <td>Using as 128=2<sup>7</sup>.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (August 2023)">clarification needed</span></a></i>]</sup> </td></tr> <tr> <td>144</td> <td></td> <td>Number expressible with two duodecimal digits. </td></tr> <tr> <td>169</td> <td></td> <td>Number expressible with two tridecimal digits. </td></tr> <tr> <td>185</td> <td></td> <td>Smallest base which is not a <a href="/wiki/Perfect_power" title="Perfect power">perfect power</a> (where generalized repunits can be factored algebraically) for which no generalized <a href="/wiki/Repunit_prime" class="mw-redirect" title="Repunit prime">repunit primes</a> are known. </td></tr> <tr> <td>196</td> <td></td> <td>Number expressible with two tetradecimal digits. </td></tr> <tr> <td>210</td> <td></td> <td>Smallest base such that all fractions <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span> terminate. </td></tr> <tr> <td>225</td> <td></td> <td>Number expressible with two pentadecimal digits. </td></tr> <tr> <td>256</td> <td></td> <td>Number expressible with eight binary digits. </td></tr> <tr> <td>360</td> <td></td> <td><a href="/wiki/Degree_(angle)" title="Degree (angle)">Degrees</a> of <a href="/wiki/Angle" title="Angle">angle</a>. </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Non-standard_positional_numeral_systems"><a href="/wiki/Non-standard_positional_numeral_systems" title="Non-standard positional numeral systems">Non-standard positional numeral systems</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=4" title="Edit section: Non-standard positional numeral systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Bijective_numeration"><a href="/wiki/Bijective_numeration" title="Bijective numeration">Bijective numeration</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=5" title="Edit section: Bijective numeration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td>1</td> <td><a href="/wiki/Unary_numeral_system" title="Unary numeral system">Unary<span class="nowrap"> </span></a>(Bijective<span class="nowrap"> </span>base‑1)</td> <td><a href="/wiki/Tally_mark" class="mw-redirect" title="Tally mark">Tally marks</a>, <a href="/wiki/Counting" title="Counting">Counting</a>. Unary numbering is used as part of some data compression algorithms such as <a href="/wiki/Golomb_coding" title="Golomb coding">Golomb coding</a>. It also forms the basis for the <a href="/wiki/Peano_axioms" title="Peano axioms">Peano axioms</a> for formalizing arithmetic within <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a>. A form of unary notation called <a href="/wiki/Church_encoding" title="Church encoding">Church encoding</a> is used to represent numbers within <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>. <p>Some <a href="/wiki/Email" title="Email">email</a> <a href="/wiki/Spam_filter" class="mw-redirect" title="Spam filter">spam filters</a> tag messages with a number of <a href="/wiki/Asterisk" title="Asterisk">asterisks</a> in an <a href="/wiki/E-mail_header" class="mw-redirect" title="E-mail header">e-mail header</a> such as <i>X-Spam-Bar</i> or <i>X-SPAM-LEVEL</i>. The larger the number, the more likely the email is considered spam. </p> </td></tr> <tr> <td>10</td> <td><a href="/wiki/Bijective_numeration#The_bijective_base-10_system" title="Bijective numeration">Bijective base-10</a></td> <td>To avoid <a href="/wiki/Zero" class="mw-redirect" title="Zero">zero</a> </td></tr> <tr> <td>26</td> <td><a href="/wiki/Bijective_numeration#The_bijective_base-26_system" title="Bijective numeration">Bijective base-26</a></td> <td><a href="/wiki/Spreadsheet" title="Spreadsheet">Spreadsheet</a> column <a href="/wiki/Numeration" class="mw-redirect" title="Numeration">numeration</a>. Also used by <a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Nash</a> as part of his obsession with <a href="/wiki/Numerology" title="Numerology">numerology</a> and the uncovering of "hidden" messages.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Signed-digit_representation"><a href="/wiki/Signed-digit_representation" title="Signed-digit representation">Signed-digit representation</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=6" title="Edit section: Signed-digit representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td>2</td> <td>Balanced binary (<a href="/wiki/Non-adjacent_form" title="Non-adjacent form">Non-adjacent form</a>)</td> <td> </td></tr> <tr> <td>3</td> <td><a href="/wiki/Balanced_ternary" title="Balanced ternary">Balanced ternary</a></td> <td><a href="/wiki/Ternary_computer" title="Ternary computer">Ternary computers</a> </td></tr> <tr> <td>4</td> <td>Balanced quaternary</td> <td> </td></tr> <tr> <td>5</td> <td>Balanced quinary</td> <td> </td></tr> <tr> <td>6</td> <td>Balanced senary</td> <td> </td></tr> <tr> <td>7</td> <td>Balanced septenary</td> <td> </td></tr> <tr> <td>8</td> <td>Balanced octal</td> <td> </td></tr> <tr> <td>9</td> <td>Balanced nonary</td> <td> </td></tr> <tr> <td>10</td> <td>Balanced decimal</td> <td><a href="/wiki/John_Colson" title="John Colson">John Colson</a><br /><a href="/wiki/Augustin_Cauchy" class="mw-redirect" title="Augustin Cauchy">Augustin Cauchy</a> </td></tr> <tr> <td>11</td> <td>Balanced undecimal</td> <td> </td></tr> <tr> <td>12</td> <td>Balanced duodecimal</td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Complex_bases"><a href="/wiki/Complex-base_system" title="Complex-base system">Complex bases</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=7" title="Edit section: Complex bases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td>2<i>i</i></td> <td><a href="/wiki/Quater-imaginary_base" title="Quater-imaginary base">Quater-imaginary base</a></td> <td>related to base −4 and <a href="/wiki/Hexadecimal" title="Hexadecimal">base 16</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98e084080c8d7213166aaefe957def03c916cc36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.901ex; height:3.009ex;" alt="{\displaystyle i{\sqrt {2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98e084080c8d7213166aaefe957def03c916cc36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.901ex; height:3.009ex;" alt="{\displaystyle i{\sqrt {2}}}"></span></td> <td>related to base −2 and <a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">base 4</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i{\sqrt[{4}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i{\sqrt[{4}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f48aaefa3cb6be4af4b2c08230fe6dfbc46ca34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.901ex; height:3.009ex;" alt="{\displaystyle i{\sqrt[{4}]{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i{\sqrt[{4}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i{\sqrt[{4}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f48aaefa3cb6be4af4b2c08230fe6dfbc46ca34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.901ex; height:3.009ex;" alt="{\displaystyle i{\sqrt[{4}]{2}}}"></span></td> <td>related to <a href="/wiki/Binary_number" title="Binary number">base 2</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd713c0f268229c4d960abe6b57f9205e4725cf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.608ex; height:2.176ex;" alt="{\displaystyle 2\omega }"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd713c0f268229c4d960abe6b57f9205e4725cf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.608ex; height:2.176ex;" alt="{\displaystyle 2\omega }"></span></td> <td>related to <a href="/wiki/Octal" title="Octal">base 8</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega {\sqrt[{3}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega {\sqrt[{3}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8760a51aec3a8be3be7ac8e05719a1a7a06efa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.544ex; height:3.009ex;" alt="{\displaystyle \omega {\sqrt[{3}]{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega {\sqrt[{3}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega {\sqrt[{3}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8760a51aec3a8be3be7ac8e05719a1a7a06efa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.544ex; height:3.009ex;" alt="{\displaystyle \omega {\sqrt[{3}]{2}}}"></span></td> <td>related to <a href="/wiki/Binary_number" title="Binary number">base 2</a> </td></tr> <tr> <td>−1 ± <i>i</i></td> <td><a href="/wiki/Twindragon" class="mw-redirect" title="Twindragon">Twindragon</a> base</td> <td><a href="/wiki/Twindragon" class="mw-redirect" title="Twindragon">Twindragon</a> fractal shape, related to base −4 and <a href="/wiki/Hexadecimal" title="Hexadecimal">base 16</a> </td></tr> <tr> <td>1 ± <i>i</i></td> <td>Negatwindragon base</td> <td>related to base −4 and <a href="/wiki/Hexadecimal" title="Hexadecimal">base 16</a> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Non-integer_bases"><a href="/wiki/Non-integer_representation" class="mw-redirect" title="Non-integer representation">Non-integer bases</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=8" title="Edit section: Non-integer bases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff4d39a9f7beda4ddbeffafaca691c386d3142cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {3}{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff4d39a9f7beda4ddbeffafaca691c386d3142cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {3}{2}}}"></span></td> <td>a rational non-integer base </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {4}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d5c72eb032bcdc52a8dc61c9a2b5da7fb49a99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {4}{3}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {4}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d5c72eb032bcdc52a8dc61c9a2b5da7fb49a99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {4}{3}}}"></span></td> <td>related to <a href="/wiki/Duodecimal" title="Duodecimal">duodecimal</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {5}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4039b80b9a1494daa03a72cb69edf66cf0a41044" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {5}{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {5}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4039b80b9a1494daa03a72cb69edf66cf0a41044" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {5}{2}}}"></span></td> <td>related to <a href="/wiki/Decimal" title="Decimal">decimal</a> </td></tr> <tr> <td><a href="/wiki/Square_root_of_2" title="Square root of 2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span></a></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span></td> <td>related to <a href="/wiki/Binary_number" title="Binary number">base 2</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {3}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {3}}}"></span></td> <td>related to <a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">base 3</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{3}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{3}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{3}]{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{3}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{3}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{3}]{2}}}"></span></td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{4}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{4}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa163183b2c3828db27e22253d454a643a4c936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{4}]{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{4}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{4}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa163183b2c3828db27e22253d454a643a4c936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{4}]{2}}}"></span></td> <td> </td></tr> <tr> <td><a href="/wiki/Twelfth_root_of_2" class="mw-redirect" title="Twelfth root of 2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{12}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{12}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc835f27425fb3140e1f75a5faa35b1e8b9efc35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.107ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{12}]{2}}}"></span></a></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{12}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{12}]{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc835f27425fb3140e1f75a5faa35b1e8b9efc35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.107ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{12}]{2}}}"></span></td> <td>usage in <a href="/wiki/12_equal_temperament" title="12 equal temperament">12-tone equal temperament</a> musical system </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7e70f0d473d5c0f14cd3c10c139f51295788fb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:3.009ex;" alt="{\displaystyle 2{\sqrt {2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7e70f0d473d5c0f14cd3c10c139f51295788fb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:3.009ex;" alt="{\displaystyle 2{\sqrt {2}}}"></span></td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {3}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5de181b9e00b86a6f2f47ff3de46d43d6a13a91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.807ex; height:5.176ex;" alt="{\displaystyle -{\frac {3}{2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {3}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5de181b9e00b86a6f2f47ff3de46d43d6a13a91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.807ex; height:5.176ex;" alt="{\displaystyle -{\frac {3}{2}}}"></span></td> <td>a negative rational non-integer base </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f922458d7d412e30c23d59dfdd457803b867508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.906ex; height:3.009ex;" alt="{\displaystyle -{\sqrt {2}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f922458d7d412e30c23d59dfdd457803b867508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.906ex; height:3.009ex;" alt="{\displaystyle -{\sqrt {2}}}"></span></td> <td>a negative non-integer base, related to <a href="/wiki/Binary_number" title="Binary number">base 2</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {10}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>10</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {10}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7409b0ddbc1f90280265e7bc95dd20626ebf1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:2.843ex;" alt="{\displaystyle {\sqrt {10}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {10}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>10</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {10}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7409b0ddbc1f90280265e7bc95dd20626ebf1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:2.843ex;" alt="{\displaystyle {\sqrt {10}}}"></span></td> <td>related to <a href="/wiki/Decimal" title="Decimal">decimal</a> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2{\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cdf91246d2cd0e905a1aaf5b4b85cfc5a5879cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:2.843ex;" alt="{\displaystyle 2{\sqrt {3}}}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2{\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cdf91246d2cd0e905a1aaf5b4b85cfc5a5879cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.261ex; height:2.843ex;" alt="{\displaystyle 2{\sqrt {3}}}"></span></td> <td>related to <a href="/wiki/Duodecimal" title="Duodecimal">duodecimal</a> </td></tr> <tr> <td><a href="/wiki/Golden_ratio" title="Golden ratio"><i>φ</i></a></td> <td><a href="/wiki/Golden_ratio_base" title="Golden ratio base">Golden ratio base</a></td> <td>early <a href="/wiki/Beta_encoder" title="Beta encoder">Beta encoder</a><sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Plastic_ratio" title="Plastic ratio"><i>ρ</i></a></td> <td>Plastic number base</td> <td> </td></tr> <tr> <td><a href="/wiki/Supergolden_ratio" title="Supergolden ratio"><i>ψ</i></a></td> <td>Supergolden ratio base</td> <td> </td></tr> <tr> <td><a href="/wiki/Silver_ratio" title="Silver ratio"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d6647fc0b70302f56dbc87eaf718dc3832ba161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.101ex; height:3.009ex;" alt="{\displaystyle 1+{\sqrt {2}}}"></span></a></td> <td>Silver ratio base</td> <td> </td></tr> <tr> <td><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)"><i>e</i></a></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span></td> <td>best <a href="/wiki/Radix_economy" class="mw-redirect" title="Radix economy">radix economy</a> <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This may be true, but without a citation, a layperson has no way of confirming this (August 2024)">citation needed</span></a></i>]</sup> </td></tr> <tr> <td><a href="/wiki/Pi" title="Pi"><i>π</i></a></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span></td> <td> </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;"><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a></span><a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/634a2acc7c8bc95cf41831ce6d74b34d3249ff46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.415ex; height:1.676ex;" alt="{\displaystyle e\pi }"></span></td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{\pi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\pi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eefb10ad1f3612be16a802dd913a9edfb5b9d823" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.258ex; height:2.343ex;" alt="{\displaystyle e^{\pi }}"></span></td> <td>Base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{\pi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\pi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eefb10ad1f3612be16a802dd913a9edfb5b9d823" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.258ex; height:2.343ex;" alt="{\displaystyle e^{\pi }}"></span></td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="n-adic_number"><a href="/wiki/P-adic_number" title="P-adic number"><i>n</i>-adic number</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=9" title="Edit section: n-adic number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Base</th> <th>Name</th> <th>Usage </th></tr> <tr> <td>2</td> <td>Dyadic number</td> <td> </td></tr> <tr> <td>3</td> <td>Triadic number</td> <td> </td></tr> <tr> <td>4</td> <td>Tetradic number</td> <td>the same as dyadic number </td></tr> <tr> <td>5</td> <td>Pentadic number</td> <td> </td></tr> <tr> <td>6</td> <td>Hexadic number</td> <td>not a <a href="/wiki/Field_(mathematics)" title="Field (mathematics)">field</a> </td></tr> <tr> <td>7</td> <td>Heptadic number</td> <td> </td></tr> <tr> <td>8</td> <td>Octadic number</td> <td>the same as dyadic number </td></tr> <tr> <td>9</td> <td>Enneadic number</td> <td>the same as triadic number </td></tr> <tr> <td>10</td> <td>Decadic number</td> <td>not a field </td></tr> <tr> <td>11</td> <td>Hendecadic number</td> <td> </td></tr> <tr> <td>12</td> <td>Dodecadic number</td> <td>not a field </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Mixed_radix"><a href="/wiki/Mixed_radix" title="Mixed radix">Mixed radix</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=10" title="Edit section: Mixed radix"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Factorial_number_system" title="Factorial number system">Factorial number system</a> {1, 2, 3, 4, 5, 6, ...}</li> <li>Even double factorial number system {2, 4, 6, 8, 10, 12, ...}</li> <li>Odd double factorial number system {1, 3, 5, 7, 9, 11, ...}</li> <li><a href="/wiki/Mixed_radix#Primorial_number_system" title="Mixed radix">Primorial number system</a> {2, 3, 5, 7, 11, 13, ...}</li> <li><a href="/wiki/Fibonorial" title="Fibonorial">Fibonorial</a> number system {1, 2, 3, 5, 8, 13, ...}</li> <li>{60, 60, 24, 7} in timekeeping</li> <li>{60, 60, 24, 30 (or 31 or 28 or 29), 12, 10, 10, 10} in timekeeping</li> <li>(12, 20) traditional English monetary system (£sd)</li> <li>(20, 18, 13) Maya timekeeping</li></ul> <div class="mw-heading mw-heading4"><h4 id="Other">Other</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=11" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Quote_notation" class="mw-redirect" title="Quote notation">Quote notation</a></li> <li><a href="/wiki/Redundant_binary_representation" title="Redundant binary representation">Redundant binary representation</a></li> <li><a href="/wiki/Goodstein%27s_theorem#Hereditary_base-n_notation" title="Goodstein's theorem">Hereditary base-n notation</a></li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric numeral systems</a> optimized for non-uniform probability distribution of symbols</li> <li><a href="/wiki/Combinatorial_number_system" title="Combinatorial number system">Combinatorial number system</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Non-positional_notation">Non-positional notation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=12" title="Edit section: Non-positional notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>All known numeral systems developed before the <a href="/wiki/Babylonian_numerals" class="mw-redirect" title="Babylonian numerals">Babylonian numerals</a> are non-positional,<sup id="cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidkXZhBAAAQBAJpgPA254_p._254:]_Chrisomalis_calls_the_Babylonian_system_"the_first_positional_system_ever"_68-0" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidkXZhBAAAQBAJpgPA254_p._254:]_Chrisomalis_calls_the_Babylonian_system_"the_first_positional_system_ever"-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> as are many developed later, such as the <a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a>. The French Cistercian monks created <a href="/wiki/Cistercian_numerals" title="Cistercian numerals">their own numeral system.</a> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 40em;"> <ul><li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">History of ancient numeral systems</a> – Symbols representing numbers</li> <li><a href="/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system" title="History of the Hindu–Arabic numeral system">History of the Hindu–Arabic numeral system</a></li> <li><a href="/wiki/List_of_numeral_system_topics" title="List of numeral system topics">List of numeral system topics</a></li> <li><a href="/wiki/Numeral_prefix" title="Numeral prefix">Numeral prefix</a> – Prefix derived from numerals or other numbers</li> <li><a href="/wiki/Radix" title="Radix">Radix</a> – Number of digits of a numeral system</li> <li><a href="/wiki/Radix_economy" class="mw-redirect" title="Radix economy">Radix economy</a> – Number of digits needed to express a number in a particular base<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Timeline_of_numerals_and_arithmetic" title="Timeline of numerals and arithmetic">Timeline of numerals and arithmetic</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_numeral_systems&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Chrisomalis2004-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Chrisomalis2004_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Chrisomalis2004_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Chrisomalis2004_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFChrisomalis2004" class="citation journal cs1">Chrisomalis, Stephen (2004). "A cognitive typology for numerical notation". <i>Cambridge Archaeological Journal</i>. <b>14</b> (1): 37–52. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0959774304000034">10.1017/S0959774304000034</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cambridge+Archaeological+Journal&rft.atitle=A+cognitive+typology+for+numerical+notation&rft.volume=14&rft.issue=1&rft.pages=37-52&rft.date=2004&rft_id=info%3Adoi%2F10.1017%2FS0959774304000034&rft.aulast=Chrisomalis&rft.aufirst=Stephen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_pp._330-333]_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFChrisomalis2010">Chrisomalis 2010</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ux--OWgWvBQC&pg=PA200">pp. 330-333</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlassBaumsSalomon2003" class="citation web cs1">Glass, Andrew; Baums, Stefan; Salomon, Richard (September 18, 2003). <a rel="nofollow" class="external text" href="https://www.unicode.org/L2/L2003/03314-kharoshthi.pdf">"Proposal to Encode Kharoṣ ṭhī in Plane 1 of ISO/IEC 10646"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Unicode" title="Unicode">Unicode.org</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Unicode.org&rft.atitle=Proposal+to+Encode+Kharo%E1%B9%A3+%E1%B9%ADh%C4%AB+in+Plane+1+of+ISO%2FIEC+10646&rft.date=2003-09-18&rft.aulast=Glass&rft.aufirst=Andrew&rft.au=Baums%2C+Stefan&rft.au=Salomon%2C+Richard&rft_id=https%3A%2F%2Fwww.unicode.org%2FL2%2FL2003%2F03314-kharoshthi.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverson2007" class="citation web cs1">Everson, Michael (July 25, 2007). <a rel="nofollow" class="external text" href="https://www.unicode.org/L2/L2007/07206-n3284-phoenician.pdf">"Proposal to add two numbers for the Phoenician script"</a> <span class="cs1-format">(PDF)</span>. <i>UTC Document Register</i>. 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L2/07-206 (WG2 N3284).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=UTC+Document+Register&rft.atitle=Proposal+to+add+two+numbers+for+the+Phoenician+script&rft.pages=L2%2F07-206+%28WG2+N3284%29&rft.date=2007-07-25&rft.aulast=Everson&rft.aufirst=Michael&rft_id=https%3A%2F%2Fwww.unicode.org%2FL2%2FL2007%2F07206-n3284-phoenician.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-Cajori-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cajori_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCajori1928" class="citation book cs1"><a href="/wiki/Florian_Cajori" title="Florian Cajori">Cajori, Florian</a> (September 1928). <a rel="nofollow" class="external text" href="https://archive.org/stream/historyofmathema031756mbp#page/n37/mode/2up"><i>A History Of Mathematical Notations Vol I</i></a>. 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(August 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">For the mixed roots of the word "hexadecimal", see <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEpp2010" class="citation cs2">Epp, Susanna (2010), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HUAIAAAAQBAJ&pg=PA91"><i>Discrete Mathematics with Applications</i></a> (4th ed.), Cengage Learning, p. 91, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781133168669" title="Special:BookSources/9781133168669"><bdi>9781133168669</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discrete+Mathematics+with+Applications&rft.pages=91&rft.edition=4th&rft.pub=Cengage+Learning&rft.date=2010&rft.isbn=9781133168669&rft.aulast=Epp&rft.aufirst=Susanna&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHUAIAAAAQBAJ%26pg%3DPA91&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span>.</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.dozenal.org/drupal/sites_bck/default/files/MultiplicationSynopsis.pdf">Multiplication Tables of Various Bases</a>, p. 45, Michael Thomas de Vlieger, <a href="/wiki/Dozenal_Society_of_America" class="mw-redirect" title="Dozenal Society of America">Dozenal Society of America</a></span> </li> <li id="cite_note-Kindra2022-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kindra2022_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKindraRogalevOsipovZlyvko2022" class="citation journal cs1">Kindra, Vladimir; Rogalev, Nikolay; Osipov, Sergey; Zlyvko, Olga; Naumov, Vladimir (2022). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Finventions7030056">"Research and Development of Trinary Power Cycles"</a>. <i>Inventions</i>. <b>7</b> (3): 56. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Finventions7030056">10.3390/inventions7030056</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2411-5134">2411-5134</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Inventions&rft.atitle=Research+and+Development+of+Trinary+Power+Cycles&rft.volume=7&rft.issue=3&rft.pages=56&rft.date=2022&rft_id=info%3Adoi%2F10.3390%2Finventions7030056&rft.issn=2411-5134&rft.aulast=Kindra&rft.aufirst=Vladimir&rft.au=Rogalev%2C+Nikolay&rft.au=Osipov%2C+Sergey&rft.au=Zlyvko%2C+Olga&rft.au=Naumov%2C+Vladimir&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Finventions7030056&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.merriam-webster.com/dictionary/septenary">"Definition of SEPTENARY"</a>. <i>www.merriam-webster.com</i><span class="reference-accessdate">. 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<span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.freepatentsonline.com/6690378.html">"Image processor and image processing method"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Image+processor+and+image+processing+method&rft_id=https%3A%2F%2Fwww.freepatentsonline.com%2F6690378.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEDasLanjewar201214-43"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEDasLanjewar201214_43-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEDasLanjewar201214_43-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEDasLanjewar201214_43-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEDasLanjewar201214_43-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFDasLanjewar2012">Das & Lanjewar 2012</a>, p. 14.</span> </li> <li id="cite_note-Nykl-44"><span class="mw-cite-backlink">^ <a href="#cite_ref-Nykl_44-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Nykl_44-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNykl1926" class="citation journal cs1">Nykl, Alois Richard (September 1926). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=1GwUAAAAIAAJ&q=Nykl&pg=RA1-PA165">"The Quinary-Vigesimal System of Counting in Europe, Asia, and America"</a>. <i><a href="/wiki/Language_(journal)" title="Language (journal)">Language</a></i>. <b>2</b> (3): 165–173. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F408742">10.2307/408742</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/408742">408742</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/50709582">50709582</a> – via <a href="/wiki/Google_Books" title="Google Books">Google Books</a>. p. 165: <q>A student of the American Indian languages is naturally led to investigate the wide-spread use of the quinary-vigesimal system of counting which he meets in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Language&rft.atitle=The+Quinary-Vigesimal+System+of+Counting+in+Europe%2C+Asia%2C+and+America&rft.volume=2&rft.issue=3&rft.pages=165-173&rft.date=1926-09&rft_id=info%3Aoclcnum%2F50709582&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F408742%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F408742&rft.aulast=Nykl&rft.aufirst=Alois+Richard&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D1GwUAAAAIAAJ%26q%3DNykl%26pg%3DRA1-PA165&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEells2004" class="citation book cs1">Eells, Walter Crosby (October 14, 2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BKRE5AjRM3AC&pg=PA89">"Number Systems of the North American Indians"</a>. In Anderson, Marlow; Katz, Victor; Wilson, Robin (eds.). <i>Sherlock Holmes in Babylon: And Other Tales of Mathematical History</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. p. 89. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-546-1" title="Special:BookSources/978-0-88385-546-1"><bdi>978-0-88385-546-1</bdi></a> – via <a href="/wiki/Google_Books" title="Google Books">Google Books</a>. <q><b>Quinary-vigesimal</b>. This is most frequent. The Greenland Eskimo says 'other hand two' for 7, 'first foot two' for 12, 'other foot two' for 17, and similar combinations to 20, 'man ended.' The Unalit is also quinary to twenty, which is 'man completed.' ...</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Number+Systems+of+the+North+American+Indians&rft.btitle=Sherlock+Holmes+in+Babylon%3A+And+Other+Tales+of+Mathematical+History&rft.pages=89&rft.pub=Mathematical+Association+of+America&rft.date=2004-10-14&rft.isbn=978-0-88385-546-1&rft.aulast=Eells&rft.aufirst=Walter+Crosby&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBKRE5AjRM3AC%26pg%3DPA89&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200:]_"The_early_origin_of_bar-and-dot_numeration_alongside_the_Middle_Formative_Mesoamerican_scripts,_the_quinary-vigesimal_structure_of_the_system,_and_the_general_increase_in_the_frequency_and_complexity_of_numeral_expressions_over_time_all_point_to_its_indigenous_development."-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidux--OWgWvBQCpgPA200_p._200:]_"The_early_origin_of_bar-and-dot_numeration_alongside_the_Middle_Formative_Mesoamerican_scripts,_the_quinary-vigesimal_structure_of_the_system,_and_the_general_increase_in_the_frequency_and_complexity_of_numeral_expressions_over_time_all_point_to_its_indigenous_development."_46-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChrisomalis2010">Chrisomalis 2010</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ux--OWgWvBQC&pg=PA200">p. 200:</a> "The early origin of bar-and-dot numeration alongside the Middle Formative Mesoamerican scripts, the quinary-vigesimal structure of the system, and the general increase in the frequency and complexity of numeral expressions over time all point to its indigenous development.".</span> </li> <li id="cite_note-Laycock_1975_219–233-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-Laycock_1975_219–233_47-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Laycock_1975_219–233_47-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLaycock1975" class="citation book cs1"><a href="/wiki/Donald_Laycock" title="Donald Laycock">Laycock, Donald</a> (1975). "Observations on Number Systems and Semantics". In <a href="/wiki/Stephen_Wurm" title="Stephen Wurm">Wurm, Stephen</a> (ed.). <i>New Guinea Area Languages and Language Study, I: Papuan Languages and the New Guinea Linguistic Scene</i>. Pacific Linguistics C-38. Canberra: Research School of Pacific Studies, Australian National University. pp. 219–233.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Observations+on+Number+Systems+and+Semantics&rft.btitle=New+Guinea+Area+Languages+and+Language+Study%2C+I%3A+Papuan+Languages+and+the+New+Guinea+Linguistic+Scene&rft.series=Pacific+Linguistics+C-38&rft.pages=219-233&rft.pub=Canberra%3A+Research+School+of+Pacific+Studies%2C+Australian+National+University&rft.date=1975&rft.aulast=Laycock&rft.aufirst=Donald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-Dibbell-48"><span class="mw-cite-backlink">^ <a href="#cite_ref-Dibbell_48-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Dibbell_48-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDibbell2010" class="citation book cs1">Dibbell, Julian (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DKPovyrXRwkC&pg=PT9">"Introduction"</a>. <i>The Best Technology Writing 2010</i>. <a href="/wiki/Yale_University_Press" title="Yale University Press">Yale University Press</a>. p. 9. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-300-16565-4" title="Special:BookSources/978-0-300-16565-4"><bdi>978-0-300-16565-4</bdi></a>. <q>There's even a hexavigesimal digital code—our own twenty-six symbol variant of the ancient Latin alphabet, which the Romans derived in turn from the quadravigesimal version used by the ancient Greeks.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Introduction&rft.btitle=The+Best+Technology+Writing+2010&rft.pages=9&rft.pub=Yale+University+Press&rft.date=2010&rft.isbn=978-0-300-16565-4&rft.aulast=Dibbell&rft.aufirst=Julian&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDKPovyrXRwkC%26pg%3DPT9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYoungFarisArmogida2019" class="citation journal cs1">Young, Brian; Faris, Tom; Armogida, Luigi (2019). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/S1872497319300997">"A nomenclature for sequence-based forensic DNA analysis"</a>. <i>Genetics</i>. <b>42</b>. Forensic Science International: 14–20. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.fsigen.2019.06.001">10.1016/j.fsigen.2019.06.001</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31207427">31207427</a>. <q>[…] 2) the hexadecimal output of the hash function is converted to hexavigesimal (base-26); 3) letters in the hexavigesimal number are capitalized, while all numerals are left unchanged; 4) the order of the characters is reversed so that the hexavigesimal digits appear […]</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Genetics&rft.atitle=A+nomenclature+for+sequence-based+forensic+DNA+analysis&rft.volume=42&rft.pages=14-20&rft.date=2019&rft_id=info%3Adoi%2F10.1016%2Fj.fsigen.2019.06.001&rft_id=info%3Apmid%2F31207427&rft.aulast=Young&rft.aufirst=Brian&rft.au=Faris%2C+Tom&rft.au=Armogida%2C+Luigi&rft_id=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS1872497319300997&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.dcode.fr/base-26-cipher">"Base 26 Cipher (Number ⬌ Words) - Online Decoder, Encoder"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Base+26+Cipher+%28Number+%E2%AC%8C+Words%29+-+Online+Decoder%2C+Encoder&rft_id=http%3A%2F%2Fwww.dcode.fr%2Fbase-26-cipher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSaxeMoylan1982" class="citation journal cs1">Saxe, Geoffrey B.; Moylan, Thomas (1982). "The development of measurement operations among the Oksapmin of Papua New Guinea". <i>Child Development</i>. <b>53</b> (5): 1242–1248. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1467-8624.1982.tb04161.x">10.1111/j.1467-8624.1982.tb04161.x</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1129012">1129012</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Child+Development&rft.atitle=The+development+of+measurement+operations+among+the+Oksapmin+of+Papua+New+Guinea&rft.volume=53&rft.issue=5&rft.pages=1242-1248&rft.date=1982&rft_id=info%3Adoi%2F10.1111%2Fj.1467-8624.1982.tb04161.x&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1129012%23id-name%3DJSTOR&rft.aulast=Saxe&rft.aufirst=Geoffrey+B.&rft.au=Moylan%2C+Thomas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span>.</span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://elementy.ru/problems/264/Bezymyannyy_palets">"Безымянный палец • Задачи"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%D0%91%D0%B5%D0%B7%D1%8B%D0%BC%D1%8F%D0%BD%D0%BD%D1%8B%D0%B9+%D0%BF%D0%B0%D0%BB%D0%B5%D1%86+%E2%80%A2+%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B8&rft_id=https%3A%2F%2Felementy.ru%2Fproblems%2F264%2FBezymyannyy_palets&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><i><a href="/wiki/Nauka_i_Zhizn" title="Nauka i Zhizn">Nauka i Zhizn</a></i>, 1992, issue 3, p. 48.</span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrannisOverhageMcDonald2002" class="citation cs2">Grannis, Shaun J.; Overhage, J. Marc; McDonald, Clement J. (2002), "Analysis of identifier performance using a deterministic linkage algorithm", <i>Proceedings. 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"World-wide user identification in seven characters with unique number mapping". <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/4082444"><i>Networks 2006: 12th International Telecommunications Network Strategy and Planning Symposium</i></a></span>. IEEE. pp. 1–5. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FNETWKS.2006.300409">10.1109/NETWKS.2006.300409</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-4244-0952-7" title="Special:BookSources/1-4244-0952-7"><bdi>1-4244-0952-7</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:46702639">46702639</a>. <q>This article proposes the Unique Number Mapping as an identification scheme, that could replace the E.164 numbers, could be used both with PSTN and VoIP terminals and makes use of the elements of the ENUM technology and the hexatrigesimal number system. […] To have the shortest IDs, we should use the greatest possible number system, which is the hexatrigesimal. Here the place values correspond to powers of 36...</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=World-wide+user+identification+in+seven+characters+with+unique+number+mapping&rft.btitle=Networks+2006%3A+12th+International+Telecommunications+Network+Strategy+and+Planning+Symposium&rft.pages=1-5&rft.pub=IEEE&rft.date=2006&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A46702639%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FNETWKS.2006.300409&rft.isbn=1-4244-0952-7&rft.aulast=G%C3%B3dor&rft.aufirst=Bal%C3%A1zs&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F4082444&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBalagaddePremchand2016" class="citation journal cs1">Balagadde, Robert Ssali; Premchand, Parvataneni (2016). <a rel="nofollow" class="external text" href="https://www.academia.edu/28219615">"The Structured Compact Tag-Set for Luganda"</a>. <i>International Journal on Natural Language Computing (IJNLC)</i>. <b>5</b> (4). <q>Concord Numbers used in the categorisation of Luganda words encoded using either Hexatrigesimal or Duotrigesimal, standard positional numbering systems. […] We propose Hexatrigesimal system to capture numeric information exceeding 10 for adaptation purposes for other Bantu languages or other agglutinative languages.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+on+Natural+Language+Computing+%28IJNLC%29&rft.atitle=The+Structured+Compact+Tag-Set+for+Luganda&rft.volume=5&rft.issue=4&rft.date=2016&rft.aulast=Balagadde&rft.aufirst=Robert+Ssali&rft.au=Premchand%2C+Parvataneni&rft_id=https%3A%2F%2Fwww.academia.edu%2F28219615&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/atomaka/base52">"Base52"</a>. <i><a href="/wiki/GitHub" title="GitHub">GitHub</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=Base52&rft_id=https%3A%2F%2Fgithub.com%2Fatomaka%2Fbase52&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://gist.github.com/csnover/1110664">"Base56"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Base56&rft_id=https%3A%2F%2Fgist.github.com%2Fcsnover%2F1110664&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/wyattisimo/base57-ruby">"Base57"</a>. <i><a href="/wiki/GitHub" title="GitHub">GitHub</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=Base57&rft_id=https%3A%2F%2Fgithub.com%2Fwyattisimo%2Fbase57-ruby&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/skorokithakis/shortuuid">"Base57"</a>. <i><a href="/wiki/GitHub" title="GitHub">GitHub</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 22,</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=Base57&rft_id=https%3A%2F%2Fgithub.com%2Fskorokithakis%2Fshortuuid&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-base58-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-base58_63-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200812103015/https://tools.ietf.org/id/draft-msporny-base58-01.txt">"The Base58 Encoding Scheme"</a>. <i><a href="/wiki/Internet_Engineering_Task_Force" title="Internet Engineering Task Force">Internet Engineering Task Force</a></i>. November 27, 2019. Archived from <a rel="nofollow" class="external text" href="https://tools.ietf.org/id/draft-msporny-base58">the original</a> on August 12, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">August 12,</span> 2020</span>. <q>Thanks to Satoshi Nakamoto for inventing the Base58 encoding format</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Internet+Engineering+Task+Force&rft.atitle=The+Base58+Encoding+Scheme&rft.date=2019-11-27&rft_id=https%3A%2F%2Ftools.ietf.org%2Fid%2Fdraft-msporny-base58&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://tantek.pbworks.com/w/page/19402946/NewBase60">"NewBase60"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=NewBase60&rft_id=http%3A%2F%2Ftantek.pbworks.com%2Fw%2Fpage%2F19402946%2FNewBase60&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160207170735/http://www.icerealm.org/FTR/?s=docs&p=base95">"base95 Numeric System"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.icerealm.org/FTR/?s=docs&p=base95">the original</a> on February 7, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=base95+Numeric+System&rft_id=http%3A%2F%2Fwww.icerealm.org%2FFTR%2F%3Fs%3Ddocs%26p%3Dbase95&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNasar2001" class="citation book cs1">Nasar, Sylvia (2001). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/beautifulmindli00nasa"><i>A Beautiful Mind</i></a></span>. Simon and Schuster. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/beautifulmindli00nasa/page/333">333</a>–6. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7432-2457-4" title="Special:BookSources/0-7432-2457-4"><bdi>0-7432-2457-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Beautiful+Mind&rft.pages=333-6&rft.pub=Simon+and+Schuster&rft.date=2001&rft.isbn=0-7432-2457-4&rft.aulast=Nasar&rft.aufirst=Sylvia&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbeautifulmindli00nasa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWard2008" class="citation cs2">Ward, Rachel (2008), "On Robustness Properties of Beta Encoders and Golden Ratio Encoders", <i><a href="/wiki/IEEE_Transactions_on_Information_Theory" title="IEEE Transactions on Information Theory">IEEE Transactions on Information Theory</a></i>, <b>54</b> (9): 4324–4334, <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0806.1083">0806.1083</a></span>, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008arXiv0806.1083W">2008arXiv0806.1083W</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTIT.2008.928235">10.1109/TIT.2008.928235</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12926540">12926540</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Information+Theory&rft.atitle=On+Robustness+Properties+of+Beta+Encoders+and+Golden+Ratio+Encoders&rft.volume=54&rft.issue=9&rft.pages=4324-4334&rft.date=2008&rft_id=info%3Aarxiv%2F0806.1083&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A12926540%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FTIT.2008.928235&rft_id=info%3Abibcode%2F2008arXiv0806.1083W&rft.aulast=Ward&rft.aufirst=Rachel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numeral+systems" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidkXZhBAAAQBAJpgPA254_p._254:]_Chrisomalis_calls_the_Babylonian_system_"the_first_positional_system_ever"-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChrisomalis2010[httpsbooksgooglecombooksidkXZhBAAAQBAJpgPA254_p._254:]_Chrisomalis_calls_the_Babylonian_system_"the_first_positional_system_ever"_68-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChrisomalis2010">Chrisomalis 2010</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kXZhBAAAQBAJ&pg=PA254">p. 254:</a> Chrisomalis calls the Babylonian system "the first positional system ever".</span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.canary-84779d6bf6-jf9pb","wgBackendResponseTime":179,"wgPageParseReport":{"limitreport":{"cputime":"1.271","walltime":"1.635","ppvisitednodes":{"value":10152,"limit":1000000},"postexpandincludesize":{"value":167109,"limit":2097152},"templateargumentsize":{"value":6869,"limit":2097152},"expansiondepth":{"value":19,"limit":100},"expensivefunctioncount":{"value":8,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":243879,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 1217.415 1 -total"," 33.74% 410.758 1 Template:Reflist"," 12.47% 151.762 7 Template:Annotated_link"," 11.07% 134.766 11 Template:Cite_journal"," 10.80% 131.492 1 Template:Numeral_systems"," 10.62% 129.320 1 Template:Sidebar_with_collapsible_groups"," 10.28% 125.098 32 Template:Cite_web"," 8.49% 103.329 17 Template:Sfn"," 6.52% 79.369 1 Template:Sidebar_with_collapsible_lists"," 5.78% 70.421 1 Template:Short_description"]},"scribunto":{"limitreport-timeusage":{"value":"0.709","limit":"10.000"},"limitreport-memusage":{"value":27389980,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREFBalagaddePremchand2016\"] = 1,\n [\"CITEREFCajori1928\"] = 1,\n [\"CITEREFChrisomalis2004\"] = 1,\n [\"CITEREFChrisomalis2010\"] = 1,\n [\"CITEREFDasLanjewar2012\"] = 1,\n [\"CITEREFDibbell2010\"] = 1,\n [\"CITEREFDonaldson2017\"] = 1,\n [\"CITEREFEells2004\"] = 1,\n [\"CITEREFEpp2010\"] = 1,\n [\"CITEREFEverson2007\"] = 1,\n [\"CITEREFEverson2011\"] = 1,\n [\"CITEREFEverson2014\"] = 1,\n [\"CITEREFEverson2016\"] = 1,\n [\"CITEREFGlassBaumsSalomon2003\"] = 1,\n [\"CITEREFGrannisOverhageMcDonald2002\"] = 1,\n [\"CITEREFGuo2009\"] = 1,\n [\"CITEREFGódor2006\"] = 1,\n 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